A nuclear physics program at the Rare Isotope Beams Accelerator Facility in Korea

Figure 1 illustrates a night sky full of bright stars on summer night seen from Seoul in 2013. Three brilliant stars that make a triangle are visible; Deneb, alpha star in Cygnus (the Swan), Vega in Lyra (the Lyre), and Altair in Aquila (the Eagle). Two birds, Cygnus and Aquila, fly through the northern sky along the Milky Way and Vega is crossing the meridian. To the south, the sky is dominated by the glowing center of the Milky Way in Sagittarius.¹ The heart of Sagittarius is known to be the core of our galaxy. In a sense, each of us has been inside a star and truly and literally consists of stardust; in a sense, each of us has been in the vast empty space between the stars. Every molecule in our bodies contains matter that once was subjected to the tremendous temperatures and pressures at the center of a star. This is where the iron in our blood cells, the oxygen we breathe, the carbon and nitrogen in our tissues, and the calcium in our bones have originated. All were formed from the fusion reactions of smaller atoms in the interior stars. The recognition of our cosmic heritage is a relatively recent achievement. The detailed understanding of this heritage combines astrophysics and nuclear physics and forms what is called nuclear astrophysics.² Here we address the following questions:

“What is the origin of these stars?”

“What makes stars shine?”

Answers to these fundamental questions can be given by Nuclear Physics; Nuclear Astrophysics and Nuclear Structure Physics.

Nuclear Physics plays a central role in our understanding of the formation of the elements in the Universe. The elements are known to be formed in the early stages of the universe as well as in hot stars. Hot stars are the live cauldrons for making atomic nuclei through nuclear reactions under high-temperature plasma conditions. Atomic nuclei produced through the stellar evolution are not limited to the few stable nuclei. Short-lived unstable nuclei are also produced through the chains of the reactions in hot stars and their explosion events. The explosive stellar events as novae, x-ray bursters, and supernovae are controlled by the properties of such short-lived radioactive nuclei.² Therefore, the understanding of the nuclear structure plays a key role in establishing the nuclear reaction rates, their mechanisms, and the origin of energy in hot stars and during their explosions.

Atomic nuclei are complex quantum-mechanical many-body systems with a finite number of nucleons; protons, Z, and neutrons, N. As a result, shell structure of the nuclei changes discretely with Z and N numbers. The question of how shell structure develops in the finite quantum many-body systems has been a common problem among various disciplines such as nuclear physics, atomic physics, condensed matter physics, molecular physics, and biophysics. The shell structure of the atomic nucleus is one of the cornerstones for a comprehensive understanding of the many-body quantum mesoscopic system. The new isotope beams offer an opportunity for approaching and mapping regions of the drip lines, and helps the study of nuclear many-body quantum stability toward the proton and neutron drip lines. The study of nuclear structure including nuclear astrophysics is going through a new era owing to the development of rare isotope beams (RIBs) accelerators and a new generation of sophisticated detector systems,

World-class accelerator facilities to produce RIBs being operated and planned in the world are: SPIRAL I and II(Système de Production d’Ions Radioactifs en Ligne) at GANIL(Grand Accélérateur National d’Ions Lourds) in France,³ RIBF (Radioactive Ion Beams Factory) at RIKEN in Japan,⁴ NSCL(National Super Conducting Cyclotron Laboratory) at Michigan State University (MSU) in USA,⁵ which will become the FRIB (Facility for RIBs) at MSU,⁶ FAIR at GSI (Gesellschaft fur Schwerionenforschung mbH) in Germany,⁷ ISAC I and II (Isotope Separator and ACelerator) at TRIUMF(Tri-University Meson Facility) in Canada,⁸ and REX and HIE-ISOLDE at CERN.⁹ 

The 2008 report of the Working Group on Nuclear Physics to the OECD's Global Science Forum stated, “The new facilities and upgrades that are now under consideration will ensure the continuing success of nuclear physics, with an estimated investment world wide of four billion US$ during the next decade. The discoveries and technical advancements that will result from the implementation of the global road-map for nuclear physics will make important contributions to other scientific fields and national and societal priorities. The forefront research facilities in the global road-map are needed to attract and train a next generation of scientists for research and national needs.”

The future of nuclear physics depends to a large extent on the planning of the new facilities. In this respect, the Korean Rare Isotope Beams Accelerator facility (here after called KRIA) stands on the heart of the future of nuclear physics in the world. This report aims to develop a concrete nuclear physics program at the KRIA facility with a goal for exploring new areas of the nuclei and the extreme areas of astrophysical nuclear reaction processes.

Figure 2 summarizes the applications of RIBs for nuclear physics. Intense and high quality RIBs allow us to address new questions about the properties of the nucleus at the limits of binding energy (mass), excitation energy, angular momentum, and isospin values. The investigation of exotic nuclei far from the stability with RIBs can offer information on all nuclear degrees of freedom: (1) proton-rich nuclei toward and beyond the proton drip line, (2) neutron-rich nuclei toward the neutron drip line, and (3) the heaviest elements and toward new super-heavy elements. The very proton-rich or the neutron-rich nuclei are the raw materials for the synthesis of the heavier elements in the universe, and thus are of considerable importance in nuclear astrophysics. The nuclei with extreme isospin values (neutron-proton asymmetries) will provide stringent constraints on the microscopic description of nuclear structure as well as nuclear dynamics.

To date, the unusual phenomena observed are: the new state of nuclear matter associated with halo and skin nuclei;¹⁰ unexpected change in magic numbers;¹¹ extremely deformed shape nuclei;¹² exotic decay including beta-delayed two neutrons or two protons emission;¹³ and two-proton or two-neutron radioactivity.¹³ Figure 3 summarizes the currently known halo nuclei, change of shell gap structures, and proton (neutron) radioactivity in a section of the nuclear chart over Z = 2 and 14. More vast information on nuclear structure can be found in other literatures.^14–20 

The locations of the nuclear shells as a function of both proton and neutron members offer incredibly valuable data that play a critical role in testing and refining the theoretical nuclear models. Within the context of the shell model, nuclear structure is understood in terms of shell orbital excitation across the shell or subshell closures. Especially, the nuclei with a few valence nucleons outside the closed shells always attract our attention for testing the various nuclear models owing to the rapidly changing nuclear structure with neutron and/or proton numbers. Therefore the nuclei near the closed shells have considerable experimental and theoretical research interest. Figure 4 illustrates a schematic view of the changes of the nuclear shell structure based on the first 2⁺ excited states in the nuclei at and near Ca, Ni, Zr, and Sn, which have large closed shells.

The so-called doubly magic nuclei with the large shell closure are: ¹⁶O(Z = 8, N = 8), ⁴⁰Ca(Z = 20, N = 20), ⁴⁸Ca(Z = 20, N = 28), ⁵⁶Ni(Z = 28, N = 28), ⁶⁸Ni(Z = 28, N = 40), ⁹⁰Zr(Z = 40, N = 50), ¹³²Sn(Z = 50, N = 82), and ²⁰⁸Pb(Z = 82, N = 126). Although the number 40 is not generally accepted as a magic number, we include ⁹⁰Zr and ⁶⁸Ni as a doubly-magic nucleus. Particularly interesting regions are around the magic numbers of Z = 20 (Ca), 28 (Ni), and 50 (Sn) protons, as they range from double magic ⁴⁰Ca, ⁵⁶Ni, and ¹⁰⁰Sn on the neutron-deficient side toward the neutron-rich side with doubly magic ⁴⁸Ca, ⁷⁸Ni, and ¹³²Sn nuclei.

For the nuclei toward the drip lines, the small additional stability comes with the filling of a particular orbital and has profound effects on their existence as bound systems, their lifetimes and structures. Thus verification of the ordering, the spacing and the occupancy of orbitals are essential in understanding how exotic nuclei evolve in the presence of large neutron/proton imbalance.²¹ 

To observe the behavior related to a fundamental characteristic of nuclear structure, it is better to draw a systematic and detailed overview of the experimental manifestation of the shell structure change over the nuclear chart as shown in Fig. 4. Especially systematic studies of the long isotones and isotopes sequences of the nuclei across the major shell closures provide stringent tests of the nuclear shell model theory.

Figure 5 describes the nuclear structure on the basis of two regimes, theory and experiment; (1) upper part shows the nuclear energy level sequences based on the shell model theory and (2) lower part shows the systematics of the first excited 2⁺ states experimentally observed in even-even nuclei as a function of proton numbers at a given neutron number.²² At first, we notice that large energy gaps are observed at ⁴⁰Ca, ⁴⁸Ca, ⁵⁶Ni, ⁶⁸Ni, and ⁹⁰Zr, which as already mentioned are known as a doubly-magic nucleus. Dynamical structural changes along the lines of Z, N = 20, 28, and 40 isotones and isotopes have been main subjects of the studies in nuclear structure physics aiming to uncover the mechanisms driving these changes, experimentally and theoretically.

Excluding characteristics of the doubly magic nuclei, we notice the following features in the energy patterns for the first excited 2⁺ states: First, shell gap at N = 20 is more pronounced at Z = 14 and 16 compared with that at Z = 18, and weakens below Z = 14 and above Z = 20. Second, the shell closure at Z = 20 (Ca isotopes) is more enhanced at N = 16 and 32. It is important to know that the shell gap at Z = 8 (O isotopes) has a semi-doubly shell closure at N = 14 and 16, respectively. According to the level sequences as shown in Fig. 5, N = 14 and 16 occupy sequentially 1d_5/2 and 2s_1/2, leading to a sub-shell gap. Similarly, N = 32 and 34 correspond to the sub-shell gap numbers that occupy 2p_3/2 and 2p_1/2 orbitals, respectively. If we follow this tendency for a shell gap, we expect that ³⁴Ca with N = 14 and ⁵⁴Ca with N = 34 would have a semi-doubly magic character. Considerable experimental and theoretical efforts are being made to answer the question of whether ⁵⁴Ca becomes a semi-doubly magic core,²³ see plan 7. The ³⁴Ca study is one of the subjects for our plans, plan 4. Third, the shell gap at N = 40 is enhanced only at Z = 28. This implies that the nuclei with neutron number 40 favor collectivity rather than individuality in ground states.¹² Fourth, proton number 40 (Zr isotopes) develops a semi-doubly magic character at N = 56 and at N = 58, which are also the sub-shell gap numbers. Interestingly, a semi-doubly shell closure also appears at Z = 64 with N = 82, namely ¹⁴⁶Gd, see Fig. 4(c).

By focusing on the harmonic oscillator shell closure numbers, namely 8, 20, 40, and 70, we find the following characteristic responses to sub-shell closures: Z = 8 responds to N = 14 and 16; Z = 20 does to N = 32 and 34 (not yet confirmed experimentally); and Z = 40 does to N = 56 and 58 for developing a semi-doubly shell closure. As noted previously, N = 14, 16, 32, 34, 56, and 58 are a family of the sub-shell gap numbers. For N = 40, we address a question of why it does not respond to Z = 32 and 34 for developing a semi-doubly shell closure. This problem may be intimately connected with the concepts of shape coexistence¹² in the corresponding ⁷²Ge (Z = 32) and ⁷⁴Se (Z = 34) nuclei. Meanwhile, both of N = 70 and Z = 70 shell numbers have no shell gap partners for developing a semi-doubly shell closure. For example, ¹²⁰Sn (Z = 50 and N = 70) shows no evidence for a semi-double shell closure, indicating that 1h_11/2 orbital remains in a strong intruder state. In this regard, it is questionable that ¹¹⁰Z (Z = 40 and N = 70) would reveal a semi-magic character.

It is important to notice that the intruder states and the associated isomers in odd Z nuclei with ±1 outside a doubly magic core provide critical information on shell structure evolution. Figure 6 demonstrates the single-particle energy level systematics on the basis of low-lying excited states for odd-Z nuclei near the doubly-magic ¹³²Sn (plan 9) and ²⁰⁸Pb (plan 10) cores. Also see Fig. 28 describing the level schemes of ¹³²Sn and ²⁰⁸Pb. It is found that the 1g_9/2, 1g_7/2, 2d_5/2, and 3s_1/2 orbitals for a region of Z = 49 and 51 and the 1h_9/2, 1f_7/2, 2d_3/2, and 3s_1/2 orbitals for a region of Z = 81 and 83 play a distinctive role in developing shell structure changes like the strength of the shell gaps and in the development of collectivity.^12,14,15 We find the following common features in this area: The first is the existence of long-lived β-decaying isomers in In and Tl nuclei. The second is a phenomenon of dynamic level changes (indicated by the blue arrows in Fig. 6) including level crossings between the ground state and the first excited state in the nuclei with +1 (Sb, Bi) and +2 (I, At) protons outside the doubly magic cores. The third is a dramatic shell structure change. For example, the 1/2⁺ level decreases rapidly in energy toward the ground level as the neutron numbers decrease and finally becomes the ground state at N = 56 in I, at N = 102 in Bi, and at N = 110 in At, respectively. The final feature is that the intruder energy levels of 9/2⁺ due to 1g_9/2 and of 11/2⁻ due to 1h_11/2 in the nuclei near ¹³²Sn show a parabolic pattern with a minimum at a specific neutron number. In contrast, for the nuclei around the ²⁰⁸Pb core, the energy levels at J^π = 11/2⁻ due to the h_11/2 orbital and at J^π = 13/2⁺ due to the i_13/2 orbital do not show such a structural behavior.

The characteristics concerned are associated with the mesoscopic nature of the nuclei such as isomerism as individuality, shape phase transitions as individuality to collectivity, and dynamic or static deformation as collectivity. The isomers observed in In and Tl can be interpreted in terms of spin-trap isomerism.^24–26 The spin trap is a common form of isomer caused by the difficulty in meeting the spin selection rule. Thereby the internal decay of the state with J^π = 1/2⁻ (9/2⁻) to the ground state with J^π = 9/2⁺ (1/2⁺) in In (Tl) isotopes is severely prohibited due to high transition multi-polarity of λ = 4.^26,27 The second picture describes the level crossing between the two proton orbitals such as 1g_7/2 and 2d_5/2 orbitals. The proton g_7/2 and h_9/2 orbitals are higher lying members of a spin-orbit doublet while the d_5/2 and f_7/2 orbitals correspond to lower-lying members, as shown in Fig. 6 where they are denoted by the green square boxes. The energy variations with the neutron numbers can be interpreted qualitatively by their energy difference that depends on the strength of the spin-orbit interactions.²⁸ Such a pattern including the level crossing is also observed in Cu (Z = 29) and Ga (Z = 31) in which the two proton orbitals based on 1f_5/2 and 2p_3/2 are crossed at a certain neutron number (see Fig. 23). The third characteristic feature is associated with the dramatic migration of the s_1/2 orbital. This picture is also observed in the isotones with N = 51. See plan 6 where we will discuss the second and third pictures in more detail.

Figure 7 shows the systematics of ground states and low-lying excited states in odd-mass C, O, and Ne (left panel) and in N = 11 isotones (right-upper panel) and Z = 11 (Na) isotopes (right-lower panel). We notice the following features: First, the variation of 2s_1/2 orbital is very dramatic as lying in the ground state at N = 9 in C and Ne while being in the first excited state in O. At N = 11, it decreases very steeply as going from Z = 10(Ne) to Z = 6(C). For Z = 8(O), it remains in the first excited states from N = 9 to N = 13. According to the spherical shell model, the s_1/2 orbital at N = 9, 11, and 13, as indicated in the level schemes in Fig. 5, generates the first excited states and then becomes the ground state at N = 15 in the respective nuclei; C, O, and Ne. It means that O isotopes keep their spherical phase in ground states. However, the situation in C and Ne is somewhat different. At N = 9, they have ground states with 1/2⁺ based on 2s_1/2 orbital. Interestingly, the dramatic change of the s_1/2 levels is also seen in isotones with N = 19, where 2s_1/2 orbital forms the ground state in ³¹Mg (N = 19). Second is associated with the appearance of the 3/2⁺ state at N = 11. We find that this 3/2⁺ state at N = 11 forms the ground states in isotones with Z = 6, 10, and 12 as well as in Na (Z = 11) isotopes with N = 10, 12, 18, and 20. On the other hand, the 5/2⁺ state based on the d_5/2 orbital at N = 11 forms the ground state in isotones with Z = 8, 14, and 16, as well as in Na isotopes (Z = 11) with N = 8, 14, and 16. We emphasize that the numbers of 14 and 16 play a critical role in developing the semi-double shell closures in O and Ca magic nuclei. By following the systematic behaviors for the 1/2⁺, 2/3⁺ and 5/2⁺ levels in isotones with N = 11, the structure of C, Ne, and Mg seems to be different in their ground states with the structure of O, Si, and S isotones. Similarly, for Na (Z = 11) isotopes, the structure of ²¹Na, ²³Na, ²⁹Na, and ³¹Na may be different in their ground states with that of ¹⁹Na, ²⁵Na, and ²⁷Na isotopes. We notice that the 1/2⁻ level based on the p_1/2 orbital becomes the ground state at N = 7 in C, O, and Ne. This is exactly consistent with the prediction of the shell model theory. It is found that this 1/2⁻ level increases in energy at N = 9 in C and O, indicating the cross of N = 8 shell gap. We will continue to discuss this subject in plan 8.

The dramatic migration (shell gap changes) of the s_1/2 level is observed in the nuclei with N, Z = 9, 11, 21, 23, 29, 31, 51, 53, 83, and 85. This characteristic is likely to be connected with the concept of a level crossing between the s_1/2 orbital and the corresponding partner orbitals with high angular momentum at a deformed phase such as ɛ₂ ∼ 0.23. In addition to the s_1/2 level characteristic, we also find a similar pattern due to the p_3/2 level in the N = 19 and/or N = 21 isotones. As will be shown in Fig. 19, the 3/2⁻ state owing to the p_3/2 orbital across the N = 28 shell closure approaches to the ground state in Mg with N = 19. Assuming that such a drop in energy continues toward the more neutron-rich side, the 3/2⁻ level would be close to the ground state in Mg as well as Ne with N = 21. This p_3/2 orbital cloud may play a role in forming halos in ³¹Ne.

To produce radioactive ion beams, there are two main approaches; ISOL production^17,29 and In-Flight production.³⁰ The KRIA accelerator has both an ISOL and fragmentation capability. Our efforts to create, separate, and study radioactive nuclides are being undertaken for the coming decade. This is an ambitious project to build a multi-beam facility capable of producing and accelerating beams of a wide mass range of nuclides with energies of a few to hundreds MeV per nucleon. See Fig. 8. The KOBRA (KOrea Broad acceptance Recoil spectrometer and Apparatus) and the IFFS (In-Flight Fragmentation Separator) facilities (see Fig. 8) will provide the selection and identification of the beam-like particles as well as target-like ones, and with the combination of a γ-ray detectors array offer spectroscopic information on internal structures of the nuclei to be investigated. The lower energy re-accelerated ISOL rare isotope beams, with energies 5 to 15 MeV per nucleon will be delivered to the low energy experimental area where they will be separated and identified by the KOBRA spectrometer. Such low energy reaccelerated RIBs are suitable for producing the nuclear reactions such as Coulomb excitations, nuclear fusion-evaporation reactions, elastic resonance scatterings, inelastic scatterings, one or two nucleon transfer reactions, and direct capture reactions. The higher energy RIBs with energies of 100 up to 250 MeV per nucleon will be produced by nuclear fragmentation at the IFFS. High quality and intense RIBs combined with re-accelerated ISOL beams including high efficient detector systems will provide unique experimental possibilities to study the very neutron-rich and proton-rich nuclei toward and beyond the drip lines.

The KOBRA and the IFFS have two complex detector systems: One is located at the target position for detection of reaction products including light-charged particles and γ rays; and the second one is positioned at focal plane for detection and identification of heavy recoiled nuclei as well as for spectroscopic study of delayed activity. Conjunction of detector systems with a polarized spin target (or polarized beam) is desirable for studying spin-orbit interactions.

The general experimental technique for nuclear physics includes mass measurements, stopped beam spectroscopy for radioactive decay, and nuclear reactions.¹⁶ 

The mass measurements allow us to obtain fundamental information on nuclear structure, nuclear astrophysics, and fundamental interactions.¹⁶ The nuclear masses are a direct reflection of the energies of the nuclei. In equilibrium, a system trends toward the lowest energy states and the transition to lower energy states releases energy, providing a source to power and to explode stars.³¹ The stability of the nuclei against the various modes of radioactive decay can easily be understood in terms of the liquid drop model mass formula: M(Z, A) = (A – Z)m_n + Z(m_p + m_e) – a₁A + a₂A^2/3 + a₃(A/2-Z)²/A + a₄Z²/A^1/3 + a₅δ(A), here a₁, a₂, a₃, a₄, and a₅ are coefficients due to volume, surface, asymmetric, Coulomb, and pairing energy terms, respectively. The pairing term δ(A) corresponds to 1/A^3/4 for odd-odd nuclei, 0 for odd-even nuclei, and –1/A^3/4 for even-even nuclei.³² 

The stopped beam β-γ spectroscopy allows us to identify and to study electromagnetic decay of isomeric and excited nuclear states, and to measure gamma rays following beta-decay of excited states into the daughter nuclei. Besides, the stopped beam spectroscopy with sophisticated detector systems offers information on exotic decay modes such as β-delayed proton(s) or neutron(s) emission in the nuclei toward the drip lines.¹³ Data on β-delayed neutron emission plays a key role in understanding the abundances of the elements as it affects the pathways of the s-process and the r-process. Both the detailed stopped beam and the in-beam spectroscopic techniques provide complementary data on the location and the ordering of single particle states for exotic nuclei of interest. They also enable us to deduce radiative neutron capture on the very neutron-rich nuclei impossible to access in direct measurements.

It is difficult and/or impossible to directly measure the thermal nuclear reaction rates based on (p, γ), (p, α), and (α, p) with RIBs such as ¹⁴O, ¹⁵O, ¹⁷F, ¹⁸Ne, ²²Mg, ²³Mg, ²⁶Al, ²⁵Si, ⁴⁴Ti, etc., because secondary beams are limited to both intensity and production from ISOL. Instead, indirect measurements based on elastic resonance scatterings, transfer reactions, and Coulomb excitations provide information on the reaction rates for a given reaction system. The cross sections for the capture reactions can be determined by Coulomb dissociation based on the inverse photo-dissociation reactions.²¹ The elastic scattering reactions are needed to study resonant states at higher excitation energies and provide information on the Coulomb amplitude and the nuclear amplitude.^16,17 The inelastic scatterings offer the properties of states in a compound nucleus where decay by particle emission to an excited state is possible. Among direct nuclear reactions, the single-nucleon removal (knockout or breakup) reactions with heavy projectile ions at intermediate energies (100 ∼ 300 MeV per nucleon) have become a specific and quantitative tool for studying single-particle occupancies and correlation effects in the nuclear shell model. Charge exchange reactions are another method to measure Gamow-Teller strength compared to the usual β–decay study. While the measurements of the β–decay are limited with Q values, the charge exchange reactions do not have such a limit. The charge exchange reactions will play another important role in studying the properties of exotic nuclei.

For nuclear astrophysics, the proposed experiments are mainly focused on the rapid proton capture reactions (rp-process) in a very hot stellar plasma (see Fig. 9). The rp-process has been known to be considerably complex due to the interplay of proton captures, decays, possibly photo-disintegrations, and particle induced reactions.³³ The important factors that influence the rp-process nuclear reaction networks above Z ≥ 32 include the proton-capture reaction rates and their inverse photo-disintegration rates, and the β-decay and electron-capture rates.³³ We should remember that nuclear deformations significantly affect the rp-process reactions.

In the following we describe the proposed experiments for the KRIA facility.

The proton drip line imposes a constraint on the reaction path of the rp-process. As shown in Fig. 10, many proton-rich nuclides near the Z = N line are unbound to proton decay. If we assume an immediate proton-decay for these proton unbound nuclei, we expect that no further proton-capture proceeds. Thus further processing depends on the β-decay of the last proton stable isotone. This bottleneck is called a waiting point. However, if the lifetime of a proton unstable nucleus is appreciably long due to a high Coulomb barrier, 2p-capture reactions on the last proton bound isotone would be possible.¹³ The 2p-capture reactions allow to bridge the single proton unstable nucleus to a proton bound nucleus as shown in Fig. 10. This two-proton capture on the last proton bound nucleus can be described by proton-capture on the intermediate proton unbound nucleus, which is produced by a resonant scattering of protons in the stellar plasma with energies above the threshold.¹³ This plan aims at measuring the 2p capture reaction rates combined with the proton resonance scatterings for the associated unbound nuclei. The 2p-capture reactions to be studied are summarized in Table I (see also Fig. 11).

In addition, we propose invariant mass measurements³⁴ for the proton unbound nuclei, such as ⁸²Mo, ⁸⁶Ru, and ⁹⁰Pd. This is because they can provide information on isospin symmetry, as well as rp-processes beyond the proton drip lines. We will discuss experimental methods for the study of the proton unbound nuclei in the following plans 2, 3, and 4.

The proposed experiments have two goals: (1) measurements of the internal structure of unbound states in ¹⁶Ne and ²⁶S and (2) measurements of the resonance states for the ¹⁴O + α system in ¹⁸Ne and the ²⁷P + p system in ²⁸S. Two-proton and/or one-proton radioactivity mechanism under the ¹⁶Ne (²⁶S) → ¹⁵F (²⁵P) + p → ¹⁴O (²⁴Si) + p + p decay conditions will be examined by drawing a three-body picture and/or two body picture for the ¹⁶Ne (²⁶S) system. This study will allow us to test a symmetry of mirror states in isobars; ¹⁶Ne (²⁶S) versus ¹⁶C (²⁶Ne) and ¹⁵F (²⁵P) versus ¹⁵C(²⁵Ne). See Fig. 12.

The proposed reactions are based on the invariant mass spectroscopic technique³⁴ for measurements of unbound states of ¹⁶Ne and ²⁶S including γ-ray measurements using the Be (¹⁸Ne, ¹⁶Ne + 2n) X and Be (²⁸S, ²⁶S + 2n) X reactions. Here X means that the final state of the target will not be measured. Through measurements of momentum transfer, we draw a resonance picture for the three-body ¹⁶Ne (¹⁴O + p + p), ²⁶S (²⁴Si + p + p) systems and for the two-body ¹⁵F (¹⁴O + p), ²⁵P (²⁴Si + p) systems.

In contrast, the invariant mass spectroscopy for the ¹⁴O + α and/or ¹⁷F + p systems in inverse kinematics with ¹⁸Ne and the ²⁷P + p system with ²⁸S provides information about the reaction rates for the ¹⁵O (α, p) ¹⁷F and ²⁷P (p, γ) ²⁸S reactions (Fig. 13).

This proposal aims to measure the unbound states of the proton radioactive ⁷³Rb through the proton elastic resonance scatterings with ⁷²Kr on a hydrogen thick target. ⁷²Kr is a waiting point where the proton capture is followed by the instantaneous emission of a proton by the proton unbound ⁷³Rb nucleus. This waiting point, however, as already pointed out, can be bypassed by a two-proton radiative capture reaction if the nucleus ⁷⁴Sr is bound. Such alternative paths can be estimated by the calculations using the properties of the intermediate unbound nucleus, ⁷³Rb. Therefore, investigation for the unbound states of ⁷³Rb nucleus is very important in this context.

As for nuclear structure studies, we investigate the shape coexistence in the proton-rich Kr nuclei with Z ≤ N. For this purpose, the proposed experiments using ^70,72Kr RIBs employ Coulomb excitation measurements which provide information on the nuclear shape built on the ground state as well as built on the first excited 0⁺ state. It is known that the ground state of ⁷²Kr would be of oblate in shape while ⁷⁴Kr and ⁷⁶Kr are known to be prolate in their ground states.^35–37 The proposed experimental methods that would require conversion electron spectroscopy are shown in Fig. 14.

The plan aims at measuring the internal structures of the proton unbound ³⁴Ca and ⁴⁸Ni nuclei with a goal for the observation of the semi doubly shell closure at Z = 20 and N = 16 in the former and of doubly-magic shell gap at Z = 28 and N = 20 in the latter. We describe the physical motivation and experimental methods for the proposed experiments by focusing on the ³⁴Ca study.

As was already pointed out, the shell closure at Z = 8 develops a semi doubly shell gap at N = 14 and 16^38,39 (see Fig. 5). Through the proposed experiment, we test whether the shell closure at Z = 20 develops a semi doubly shell gap at N = 14 beyond the proton drip line. Another motivation of the proposal is to examine the two-proton radioactivity mechanism for the ³⁴Ca → (³³K + p) → ³²Ar + 2p decay system. Through another breakup channels with the same reaction system, the excited states in odd proton-rich ³³K and ³⁵K nuclei are also measured. The investigation of ³³K and ³⁵K aims at testing isospin symmetries between mirror nuclei. In addition, the one-proton removal cross section of ³⁶Ca enables us to obtain the astrophysical factor for the proton radiative capture reaction of ³⁵K (p, γ) ³⁶Ca.

To date, no properties of ³⁴Ca have been observed experimentally. This is largely because it is a proton unbound beyond the drip line. Only the upper lifetime limit, T_1/2 < 35 ns has been reported.²² Figure 15 demonstrates the level and decay scheme for the three-body ³⁴Ca system. It is predicted from the AME2012 mass surface systematics⁴⁰ that the two- and one-proton separation energies of ³⁴Ca would be S_2p = −1470(300) keV and S_p = 480(360) keV, respectively. Hence, with a positive one-neutron separation energy and a negative S_2p, the ground state is likely to decay via a two-proton radioactivity such that ³⁴Ca corresponds to a true two-proton emitter. For the 2⁺ excitation energy, however, as shown in Fig. 15 the decay should evolve sequentially through the intermediate states in the two-body system, i.e., ³³K + p. Here the expected energy for the 2⁺ state was obtained with the systematic consideration based on the 2⁺ level energies found in the neighboring nuclei. Notice that ³³K has been known to be proton unbound as well. We expect that the investigation of proton decay mechanism for the ³⁴Ca system provides unprecedented insights into exhibiting the new forms of radioactivity.

The first case of 2p radioactivity was in the decay of ⁴⁵Fe at GSI and at GANIL in 2002.¹³ However, the first direct observation of the two protons ejected from ⁴⁵Fe was achieved in 2007 by recording projections of proton's tracks on the anode plane of the TPC (time projection chamber).^13,41 The full correlation picture for the 2p decay of ⁴⁵Fe was established in the experiment at NSCL MSU.⁴² 

Figure 16 shows the experimental results for the three-body ⁴⁵Fe system and the related theoretical calculations.¹⁵ From the theoretical analyses for the momentum density distribution on the kinematical plane, the correlation pictures were found to be good agreement with the three-body model. Through the proposed experiment, we will draw a three-body picture for the ³⁴Ca system. If we observe a strong diproton-like correlation between the two protons emitted in the decay of ³⁴Ca, we would gain some insights into a presence of the p-p virtual state in the three-body decay process.

The proposed experiment are based on a ⁹Be (³⁶Ca, ³⁴Ca + 2n) X reaction and aims at measuring the unbound states in proton unbound ³⁴Ca. The ³⁴Ca ions will be produced by a two-step process. First, the ³⁶Ca ions will be selected from the fragmentation products of the primary ⁴⁰Ca beam on ⁹Be target, and transmitted to the zero degree spectrometer. There, by two-neutron knockout reactions in a secondary ⁹Be target, ³⁴Ca ions will be created and will subsequently decay in-flight within a few meters after leaving the target. Identification of the unbound states will require a sophisticated spectroscopic study employing coincidence measurements of ³²Ar, ³³K, protons, and/or neutrons combined with γ-ray detections. The measurements of momentum transfer with respect to the three-body decay (³²Ar + p + p) enable us to draw a resonance picture of the ground and/or first excited state for ³⁴Ca. In addition, through such an invariant mass spectroscopy, unbound ³³K nucleus, the two-body decay (³²Ar + p) can be investigated as well. The in-beam γ-ray spectroscopy combined with the invariant mass spectroscopy proves the correctness of the invariant mass measurements and provides information of decay patterns in the respective nuclei. Figure 17 illustrates a schematic view of the experimental setup for the proposal.

The separate detection of two emitted protons and the measurement of their momenta are essential. From the measured energy and angle of the protons and the ³²Ar nuclei, the invariant mass of ³⁴Ca (M_34Ca) can be calculated. Then the three-body energy can be calculated as E_T = [M_34Ca – M_32Ar – 2M_p]c², where M_32Ar is the rest mass of ³²Ar and M_p is the proton mass. The determination of the energy and angular correlations between the emitted two protons will be very important. The correlations of the two protons are theoretically expected to be three types: diproton decay, three-body decay, and phase volume decay. The limiting cases are the emission of a diproton cluster, which is a correlated pair in a diproton-like decay and the phase-space decay where the protons exhibit no correlations. Examination of such correlations in the three-body system provides insight into different modes of the decays.¹³ 

As an example, we introduce a recent experimental result for the measurements of three-body correlations in the ⁶Be (α + p + p) system which is located beyond the proton drip line.⁴³ Figure 18 shows the experimental setups and its invariant mass spectrum for the ⁹Be system.⁴³ As shown in Fig. 18, the 0⁺ and 2⁺ resonances were clearly identified.

The proposed experiment aims at measuring the internal structures of proton-rich ⁴¹Ti, ⁴⁴Cr, and ⁴⁵Cr nuclei to test the symmetry of mirror states in isobaric A = 41, 44 and 45 by comparing with the structures of ⁴¹K, ⁴⁴Ca, and ⁴⁵Sc. The nuclei of interest are produced through a one (or two) neutron knockout reaction of secondary beams on a thick ⁹Be target. The secondary beams are produced by the fragmentations of a 250 MeV per nucleon ⁷⁸Kr primary beam on a thin ⁹Be production target. The proposed reactions are as follows: ⁹Be (⁴²Ti, ⁴¹Ti + n) X for ⁴¹Ti, ⁹Be (⁴⁶Cr, ⁴⁴Cr + 2n) X for ⁴⁴Cr, ⁹Be (⁴⁶Cr, ⁴⁵Cr + n) X for ⁴⁵Cr, and ⁹Be (⁴⁶Cr, ⁴⁵V + p) X for the indirect measurements of the ⁴⁵V (p, γ)⁴⁶Cr reaction rate. The γ-ray spectroscopy employs to measure the internal electromagnetic transitions in the nuclei of interest.

The goals of the proposal are: (1) Identification of E(2⁺) and E(4⁺) in even-even ⁴⁴Cr for investigating the magic N = 20 shell evolution like an emergence of collectivity; (2) measurements for the low-lying excited states in odd-Z ⁴¹Ti and ⁴⁵Cr for testing charge symmetry between mirror nuclei, Z, N = 19 and 21 with A = 41 and 45; (3) Search for isomers in the nuclei of interest to study the single-particle and collective features based on isomerism; and (4) measurement of the ⁴⁵V (p, γ) ⁴⁶Cr reaction rate through the projectile-like ⁴⁶Cr breakup reaction for estimating nucleosynthesis of ⁴⁴Ti.

Nuclear Structure: Figure 19 illustrates the partial single-particle energy level diagram and the energy level systematics for the ground and low-lying single-particle excited states in Z = 19 and 21 nuclei as a function neutron numbers and in N = 19 and 21 as a function of proton numbers. This proposal is focused on the proton rich side. The neutron-rich side will be investigated with plan 7. In the region of Z, N = 19 and 21, the 2s_1/2, 1d_3/2, 1f_7/2, and 2p_3/2 orbitlas play a critical role in the strength of the shell gaps as shown in Fig. 19. We find the following distinctive features: First, for Z = 19 isotopes, the 1/2⁺ level due to 2s_1/2 subshell decreases rapidly with increasing neutron numbers from N = 20 and finally becomes the ground state at N = 28. For N = 19 isotones the subshell also decreases toward ground level with decreasing proton numbers from Z = 20 and finally becomes the ground state at Z = 12. We notice that the nuclei at and below Z = 12 turned out to be deformed in their ground states at magic neutron number 20.^11,17 Second, for Z or N = 19, the 7/2⁻ level due to the 1f_7/2 subshell forms isomers with half-lives of a few nanoseconds across the 20 magic gap region as an intruder state. Third, for Z and N = 21, the 3/2⁺ level due to 1d_3/2 subshell changes dramatically with neutron and proton numbers and forms isomers near the ground states at N = 22, 24 and Z = 22. This proposal, as well as a proposal associated with searching for the proton unbound ³⁴Ca nucleus (plan 4), aims at proving the charge symmetries by observing low-lying states in isobars with Z, N = 19 and 21 toward Z > 20 and N < 18. Besides, we are interested in searching for isomers in ⁴¹Ti and ⁴⁵Cr as denoted in Fig. 19.

Nuclear Astrophysics: The second goal of this plan is to measure thermal nuclear reaction rates for the ⁴⁵V (p, γ) ⁴⁶Cr reaction. This reaction is one of the key paths responsible for the ⁴⁴Ti production detected in our Galaxy. The space-based γ–ray telescopes such as INTEGRAL,⁴⁴ have detected γ rays of cosmic origin. Such a gamma-ray line provides a direct evidence that nucleosynthesis is an ongoing process in our galaxy. Figure 20 shows the detected γ-ray distributions following β-decay of unstable isotopes, such as ²⁶Al, ⁴⁴Ti and ⁵⁶Ni. The evidence of nucleosynthesis of ⁴⁴Ti has been based on the observation of 68, 78, and 1157 keV γ–ray lines which are emitted through the β⁺ decay of ⁴⁴Ti (T_1/2 = 58.9 ± 0.3 yr) to its daughter ⁴⁴Sc nucleus and finally to ⁴⁴Ca. Such a gamma-line flux comes from the Cassiopeia A supernova remnants⁴⁵ and also the Vela ones.⁴⁶ Therefore, the ⁴⁴Ti nuclide is considered an important signature of core-collapse supernova nucleosynthesis and an isotope of extraordinary astrophysical significance.⁴⁷ 

The nucleus ⁴⁴Ti is believed to be produced during the α–rich freeze-out by α capture on ⁴⁰Ca, namely the ⁴⁰Ca (α, γ) ⁴⁴Ti reaction in supernova environment. However, the nuclear reactions involved in the production of ⁴⁴Ti are complicated. The ⁴⁴Ti production was known to be most sensitive to the ⁴⁴Ti (α, p) ⁴⁷V, α (2α, γ) ¹²C, ⁴⁴Ti (α, γ) ⁴⁸Cr, and ⁴⁵V (p, γ) ⁴⁶Cr reactions rates. The analyses for the influence of individual reaction rates on the ⁴⁴Ti production showed that the ⁴⁵V (p, γ) ⁴⁶Cr reaction rate made a large impact on the ⁴⁴Ti abundances in α–rich freeze-outs within the supernova events.⁴⁷ Until now, no experimental measurements for the reaction rates of this reaction have been made. See Fig. 21.

Experiments: Under the reaction conditions when the fast projectiles collide peripherally with a light nuclear target, the residue final state energy can be determined by measuring coincidences with the γ-rays emitted from the in-flight decay. It has been shown that the longitudinal component of the momentum along the beam line gives the most accurate information on the intrinsic properties of loosely bound nucleon(s) and that is insensitive to details of the collision and the size of the target.⁴⁸ In contrast, the transverse distributions of the core are significantly broadening by diffractive effects and by Coulomb scattering.³⁰ To understand the measured longitudinal momentum distribution it is necessary to take into account that the external part of the nucleon wave function contributes to mainly inducing a heavy-ion knockout reaction, as being surface dominated. The magnitude of the reaction cross section is determined by the part of the wave function that is accessed, and the shape of the momentum distribution reflects the momentum content in this part.^49–56 

In nuclear astrophysics, the direct measurements of the thermal nuclear reaction rates are essential. In many cases, however, such direct measurments involving unstable nuclei are very difficult or even impossible and indirect methods must be used. For a long time the nuclear transfer reactions have been well known to be used as one of the indirect methods for nuclear astrophysics.⁵⁷ Recently, one-nucleon knockout (or breakup) reactions offered an alternative and complementary technique for extracting the asymptotic normalization coefficients (ANCs) that was particularly well adapted to RIBs using fragmentation at intermediate energies.^48,58–60

One-nucleon knockout reactions are powerful spectroscopic tools to determine the single-particle structure of the nuclei far from the stability. This is because the shapes of the momentum distributions of the core fragments measured in such knockout reactions provide information of the orbital angular momentum of the removed nucleon, whereas the nuclear knockout cross section determines the ANCs. And the ANCs are used to calculate the direct non-resonant component of the astrophysical S factor of the radiative capture reaction.^49,50 Here we employ one-proton knockout reaction with the ⁴⁶Cr beam to evaluate the ⁴⁵V (p, γ) ⁴⁶Cr reaction rate. Through this reaction, the cross section and momentum distribution of the ⁴⁵V residue from the one proton removal of ⁴⁶Cr will be measured and compared to Glauber type calculation. This enables us to deduce the corresponding spectroscopic factor and determine the ANCs for the ⁴⁶Cr → ⁴⁵V + p system. The ANCs are then employed to evaluate the non-resonant component of the astrophysical S factor for ⁴⁵V (p, γ) ⁴⁶Cr. By detecting individual γ-rays in coincidence with the residual ⁴⁵V selection, we measure the inclusive and exclusive longitudinal momentum distributions of the ⁴⁵V knockout fragments and the corresponding differential and integral knockout cross sections. In addition, the invariant mass measurements for the ⁴⁵V + p system provide information on isobaric states associated with the resonance peaks in the continuum states, as shown in Fig. 26, above the reaction threshold of ⁴⁵V.

This plan aims at investigating the vicinity of the two magic members of Z = 28 and N = 50. The study of doubly magic ⁷⁸Ni has been pursued for a long time and is still an object of active experimental and theoretical researches. With two and four protons outside the Z = 28 proton shell closure, Zn and Ge isotopes form an interesting set nuclei to study the evolution of nuclear structure near the proton Z = 28 and neutron N = 50 shell closures. In neutron-rich Cu, Zn, Ge, Ga, and Se isotopes over N ≥ 50, neutrons begin to occupy the 2d_5/2, 3s_1/2 and/or 1g_7/2 orbitals cross over the 1g_9/2 orbital, which separates N = 40 subshell and the N = 50 shell gaps. See Fig. 22.

The proposed experiments are based on the measurements of β-decay lifetimes and isomers for studying the internal structure of the very neutron rich nuclei with Z = 29 to 35 and N > 50. The nuclei to be investigated will be produced following the stopped beam formed by the fission fragmentation between a ²³⁸U beam with 250 MeV per nucleon and a ⁹Be production target. The measurements are as follows: (1) Spin-parity assignments to the ground state and/or the first excited state in odd-N ⁷⁹Ni, ^81,83Zn, ^83,85Ge, and ^85,87,89Se for investigating effects of the neutron single-particle orbital migration on the shell evolution; (2) spin-parity assignments to the ground state and the first excited state in odd-Z ^79,81Cu, ^83,85Ga and ^85,87As for investigating effects of the proton single-particle orbital migration on the shell evolution; (3) identification of E(2⁺) and/or E(4⁺) in even-even ^78,90Ni, ^80,82Zn, ^84,86,88Ge, and ^88,90Se for investigating the ⁷⁸Ni core shell evolution; and (4) search for isomers in the nuclei of interest to study the single-particle and collective features based on the isomerism.

Concerning the N = 50 shell evolution, many studies^61–63 established a systematic decrease of the energy difference between the lowest 5/2⁺ and 1/2⁺ levels, attributed to the population of single-particle d_5/2 and s_1/2 orbitals as shown in Fig. 22. The ground state of these nuclei are assigned as J^π = 5/2⁺, because of occupation of the neutron d_5/2 subshell.⁶² Taking an extrapolation of the N = 51 systematic as shown in Fig. 22(d), we expect that there would be a possibility of the level crossing between the d_5/2 and s_1/2 orbitals. Such a scenario in fact was suggested in,⁶⁴ which postulated a 1/2⁺ ground state spin assignment for ⁸¹Zn. However, Padgett et al.⁶¹ claimed that the experimental data for the β-decay of ⁸¹Zn do not support such a spin-inversion hypothesis along with the shell model calculations including the details of the proton-neutron interactions. Only experiments for measuring the internal structures of ⁸¹Zn and ⁷⁹Ni are able to provide information on the level crossing between the d_5/2 and s_1/2 orbitals.

For the neutron-rich odd-Z nuclei toward the doubly magic ⁷⁸Ni, we also find a dramatic level change in the 5/2⁻ level due to the πf_5/2 orbital. As shown in Fig. 23(a), the 5/2⁻ level drops rapidly down in ^71,73Cu⁶⁵ and becomes the ground state in ⁷⁵Cu.⁶⁶ Such a dramatic migration is also observed in Ga isotopes as shown in Fig. 23(b), where the crossing between the 5/2⁻ and 3/2⁻ levels occurs at N = 48. The migration of the 5/2⁻ level, leading to the level inversion of the πp_3/2 and πf_5/2 orbitals, has been interpreted as being attributed to a strong attractive monopole interaction that becomes active when neutrons occupy the νg_9/2 orbital.⁶⁷ One of the physics mechanisms driving these monopole shifts was suggested tobe the tensor part of the residual nucleon-nucleon interactions.^68,69

The proposed experiments provide direct information on shell evolution of the ordering of p_3/2, f_5/2, and p_1/2 states beyond the g_9/2 neutron occupation. See Figs. 23 and 24.

Now we discuss in more detail about the associated nuclear structure with subshell migration and its occupation. As was already shown, the proton f_5/2 and p_3/2 levels are inverted when a pair of neutrons cross over N = 44 (in Cu) or N = 48 (in Ga and As). Thereby for neutron-rich Ni, Zn, and Ge, protons occupy the f_5/2 subshell at Z = 29 to 34 and then occupy the p_3/2 subshell at N = 38, and finally occupy the p_1/2 at N = 40. We emphasize that the f_5/2 subshell has a capacity of 6 protons (3 pairs of protons); 30, 32, and 34. It is well known that a half occupation filled up to midshell in a high-j orbital gives rise to driving the nucleus toward deformation. Taking into consideration that Z = 32 (Ge) has a number of a half occupation in the f_5/2 orbital, Ge would have a more deformed shape than its neighboring nuclei beyond N = 50. As evident in Fig. 23(d), we also find that such an energy minimum, indicating a deformation phase, occurs at Z = 44(Ru) or Z = 46(Pd). This aspect comes from the result of the half-occupation of the g_9/2 subshell. For confirming the present scenario, the experiments for identifying the 2⁺ state and/or the 4⁺ state in Ge, Se, and Kr over N = 54 and 56 are required. See plan 7.

Next, we focus on another characteristic feature revealed in the systematics of the first 2⁺ states in Ni, Zn, Ge, Se, and Kr isotopes (see Fig. 23(d)). Within the range of N = 34 to 48 the level patterns are divided into two regimes; one is built on Zn and Ge and the other is built on Kr. The Se nucleus shows a transitional character. Removing a level line of the Se isotopes, one can see a clear difference between these two regimes as shown in Fig. 25. More importantly, we find a distinctive change of the 2⁺ level energy in Kr isotopes between N = 38 and 36. This shell structure change is considered to be related with shape phase transition; prolate and oblate in their ground states.^35,37 In this respect, it is important to identify the levels of 2⁺, 4⁺, 0₂⁺, 2₂⁺, and 4₂⁺ states in ⁷⁰Kr, ⁷²Kr, and ⁶⁶Se. See plan 3 where we discussed the measurements for the excited states of ⁷⁰Kr and ⁷²Kr.

For now a natural question arises, “why does the Se have a transitional character ?”. An answer can be made by the proton subshell occupation arguments. As shown in Fig. 23(c), the Se's proton number 34 is positioned at the boundary of the proton f_5/2 and p_3/2 subshells. According to the level systematics for Cu and Ga as in Figs. 23(a) and 23(b), the neutron-rich Se isotopes occupy fully the f_5/2 subshell since the first subshell above Z = 28 becomes the f_5/2 orbital. In contrast the neutron deficient isotopes occupy partially the f_5/2 subshell after filling the p_3/2 orbital. It is apparent that the Kr and the Ge isotopes occupy the second subshell (f_7/2) and the first subshell (p_3/2), respectively. Such a difference in occupation of the subshells would bring out a different character between Ge (Z = 32) and Kr (Z = 36). Accordingly, the transitional aspect for the Se nucleus is likely due to a mixing effect caused by a correlation between the proton f_5/2 and p_3/2 orbitals. Following this conjecture, the patterns of the level structures are expected to be different in the respective Ge, Se, and Kr nuclei beyond N = 50.

This plan aims at exploring single-particle shell migrations in the vicinity of ⁵²Ca and ⁵⁴Ca. The experiments are based on the nucleon removal (knockout) reactions using the IFFS to be installed in the high energy experimental area. The proposed one-proton removal reactions are as follows: ⁹Be (⁵⁰Ca, ⁴⁹K + p) X, ⁹Be (⁵²Ca, ⁵¹K + p) X, ⁹Be (⁵⁴Ti, ⁵³Sc + p) X, and ⁹Be (⁵⁶Ti, ⁵⁵Sc + p) X. This proposal has a goal for studying the internal structure of very neutron rich nuclei with Z = 19 and 21 and N ≥ 30; ⁴⁹K, ⁵¹K, ⁵³Sc, and ⁵⁵Sc. The measurements involve the thick reaction target ⁹Be and the γ-ray spectroscopy of the projectile-like residual nuclei for the final state resolution. The residual nuclei are produced through the one-proton knockout reactions on a ⁹Be target by the secondary rare isotopes beams produced from the fragmentation between a ⁸⁶Kr primary beam with 250 MeV per nucleon and a ⁹Be production target.

Figure 26 displays the single-proton energy levels for Z = 19 (K) and 21 (Sc) as a function of neutron numbers. As shown in this figure, the 2s_1/2, 1d_3/2 and 1f_7/2 subshells contribute dominantly to shell structure evolution in proton-single levels. In contrast, neutrons begin to occupy the 2p_3/2, 2p_1/2 and/or 1f_5/2 orbitals cross over the 1f_7/2 orbital, which separates the N = 20 gap and the N = 28 gap.

As was already discussed, for Z = 19 isotopes the 1/2⁺ level due to 2s_1/2 subshell decreases remarkably with increasing neutron numbers and finally becomes ground state at and beyond N = 28. For Z = 21 isotopes, the 3/2⁺ level due to 1d_3/2 subshell changes dramatically as it goes down to near the ground state at N = 24. It is interesting to notice that the levels of 3/2⁺ and 1/2⁺ are inverted at N = 28 in Z = 19 (⁴⁷K) and Z = 21 (⁴⁹Sc).

The inversion of the 3/2⁺ and 1/2⁺ levels, however, is uncertain in ⁴⁹K and unknown in ⁵³Sc and ⁵⁵Sc above N = 28. It is worthwhile to remind that N = 32 and 34 develop the semi-double shell gaps with Z = 20. We address how the distinctive quasiparticle levels, such as 2s_1/2, 1d_3/2, and 1f_7/2 migrate and make an impact on the formation of the semi-double shell closure of ⁵⁴Ca. The migration of the proton 2s_1/2, 1d_3/2, 1f_5/2 levels as well as the neutron 2p_1/2, 1f_5/2 levels with respect to neutron numbers may indicate an underlying physics not well accounted for in the present shell model interactions. In this regard, the present proposal is an important step toward extremely neutron-rich region where more exotic phenomena including halos or skins are expected.

This plan aims at investigating the single particle level structure for the nuclei with Z = 9 and N = 14 and N = 16, and with Z = 14 and N = 9 for understanding the shell model mechanism forming the semi-double shell closure. In addition, the measurement of the excited states of ²³Si gives a hint for the presence of a symmetry due to isospin interaction under a large Z/N ratio by comparing with the structure of ²³F (Z = 9, N = 14).

Figure 27 shows systematics of the ground states and the low-lying excited states in isotopes with Z = 9, 11 and isotones with N = 9, 11. As far as shell structure stabilization is concerned, it is surprising that a dramatic jump in stability occurs between Z = 8 (O) and Z = 9 (F) by adding one proton so that the location of the neutron drip line extends an extra six neutrons from ²⁴O to ³¹F. Such an enhanced stability of the neutron-rich fluorine isotopes could be attributed to a broken of N = 20 shell gap and thus the increased contribution from a correlation due to the large fp-shell occupancy.³⁵ 

As shown in Fig. 27, the level energies associated with 2s_1/2, 1d_3/2, 1p_1/2, and 1p_3/2 orbitals are minimized at N = 10 for F isotopes and at Z = 10 for isotones with N = 9, and increase steeply toward N = 14 for F. As was pointed out earlier, the emergence of the 3/2⁺ state at and near the ground state at N, Z = 11 attracts our attention since it lies at the ground state in the N = 11 isotones with Z = 6, 10, and 12 and in the Z = 11 isotopes with N = 10, 12, 18, and 20. In contrast, the 5/2⁺ state owing to the d_5/2 orbital forms the ground state in the N = 11 isotones with Z = 8, 14, and 16 and in the Z = 11 isotopes (Na) with N = 8, 14, and 16. Experimental information of the shell structure for the neutron-rich and proton-rich nclei with N, Z = 14 and 16 is very scarce along a chain of Z = 9 and N = 9, and is only known in the case of F with N = 14. For investigating the subshell gap changes associated with the semi doubly shell closure in this region, the measurements of the internal structures of the ^25,27F and ²³Si nuclei are highly desirable. Furthermore, the experiment for the level structure of ²³F and ²¹Mg is needed to construct the systematic trends. The proposed experiments are: First, transfer reactions with energies at a few MeV per nucleon; d (²⁶Ne, ³He) ²⁵F for ²⁵F, p (²⁴Si, d) ²³Si for ²³Si, and p (²²Mg, d) ²¹Mg for ²¹Mg. Second, one or two nucleon knock-out reactions with energies at 200 MeV per nucleon including gamma-ray spectroscopy; ⁹Be (²⁹Na, ²⁷F + 2p) X and p (²⁸Ne, 2p) ²⁷F for ²⁷F and ⁹Be (²⁵Si, ²³Si + 2n) X and p (²⁴Si, p+n) ²³Si for ²³Si.

The double magic core of ¹³²Sn is a starting point in investigating the behavior of the Z = 50 and N = 82 shell closure for even more neutron-rich nuclides. The 2⁺ level of ¹³²Sn is a remarkable doubly closed-shell structure (See Fig. 4(c)). To compare the shell closure of the double magic shell gaps of Z = 50, 82 with N = 82, 126, we plotted the partial level schemes of ¹³²Sn and ²⁰⁸Pb in Fig. 28. As evident in this figure, the > 4 MeV gap to the first excited state of ¹³²Sn is much larger than the gap of doubly magic ²⁰⁸Pb with its 2.6 MeV gap, exhibiting the strongest shell closure of any nucleus heavier than ¹⁶O.¹² For ²⁰⁸Pb the first excited level at J^π = 3⁻ is known to be a highly collective octupole state.

This plan aims at investigating the neutron rich nuclei around Z = 50 that would reveal the changes of size, diffuseness, and shell closures with the increase of neutron numbers toward and beyond N = 82. Figure 29 displays the energy level patterns based on the 2⁺ states in even-even nuclei with Z = 46 (Pd) to 54 (Xe) as a function of neutron numbers. Interestingly, the shell structures are divided into two groups within the region of N = 56 and N = 74; one is based on the nuclei with ±2 and the other is based on the nuclei with ±4 protons outside the Z = 50 shell closure. This specific characteristic arises from the nature of N = 64 shell gap. The N = 64 sub-shell gap is only stabilized for producing a semi-double shell closure at Z = 50 and becomes weakened as it goes away from Z = 50. As shown in Fig. 29, there is no indication revealing N = 64 shell gap effect in Xe and Pd that have ±4 protons outside Z = 50. The parabolic pattern with its minimum value at N = 66 or 68 for Xe and Pd clearly indicates a regime dominated by the high-j intruder h_11/2 orbital. It is worthwhile to notice that a similar pattern is seen in the vicinity of N = 40 as in Fig. 23(d).

Figure 30 summarizes shell structure description based on the ground states and the low-lying excited states in the isotones along N = 79 to 89. One can see that an abrupt change of the specific subshell orbitals such as d_3/2 and h_11/2 occurs in neutron rich nuclei, such as Pd and Ru with N = 79 and 81. Focusing on the systematics for N = 85 and 87 isotones, one can observe that the 2/3⁻ state is maximized at Z = 64 (Gd) while the 7/2⁻ state is maximized at Z = 56 (Ba). As was emphasized earlier, the numbers of 56 and 64 correspond to subshell gaps. Notice that the ¹⁴⁶Gd nucleus shows a semi-double magic characteristic as shown in Fig. 3.

The planned experiments are based on multi-nucleon transfer and the one-or-two nucleon removal (knockout) reactions of ¹⁴⁴Xe on a Be target or a Pb target. The ¹⁴⁴Xe beam will be produced by the reaccelerated RIBs from the ISOL. Through this plan, we will study the collectivity associated with shape phase transitions in the neutron-rich Xe and Ba nuclei. For this purpose, the experiments employ Coulomb excitation measurements and stopped-beam decay measurements. The Coulomb excitations allow us to extract matrix elements for the octupole correlations in the nuclei of interest, such as ^144,146Xe and ^144,146,148Ba nuclei, etc. The proposed experimental results provide an evidence of the existence of octupole correlations, indicating static deformation⁷¹ in this region.

This region is a section of the nuclear chart that is not easy to access under current experimental condition. In particular, both the north-eastern area and the south area of the Z = 82 and N = 126 point remain mostly unexplored. Figure 31 demonstrates the energy level systematics of the first excited 2⁺ states in the nuclei around the doubly magic ²⁰⁸Pb core. For the energy levels of Pb isotopes the nuclear structures in neutron deficient isotopes evolve as in the followings:⁷² First, from ²⁰⁸Pb to around ²⁰⁰Pb (N = 118), the first excited 2⁺ states are spherical. Second, for isotopes below ²⁰⁰Pb, a lower-lying excited 0⁺ state appears and is interpreted as a two particle-two hole (2p-2h) intruder state with a small oblate deformation. This is a case of shape coexistence. Third, below ¹⁹⁰Pb with N = 108, the structural picture changes again so that the states above the first excited 2⁺ level reveal a rotational band. These rotational states are interpreted as ones being built on a 4p-4h intruder state with a large prolate deformation. This is the best case for exhibiting a triple shape coexistence, i. e., spherical, oblate, and prolate in a nucleus. The triple 0⁺ states were also observed in neutron deficient Hg nuclei.⁴⁹ The measurements of E0 matrix elements employing the conversion electron and the γ-ray spectroscopic techniques are essential for obtaining direct information on the shape coexistence and its configuration mixing.

As a starting point to study shell structure evolution based on the single particle configurations over Z = 82 and N = 126, we focus on investigating the level structures of Tl (Z = 81) and Bi (Z = 83) because the intruder states and the associated isomers in odd Z nuclei with ±1 outside doubly magic core provide critical information on the shell structure evolution. The single-particle energy level systematics based on the low-lying excited states for odd-Z nuclei just around ²⁰⁸Pb were already shown in Fig. 6.

By considering the currently known nuclei, we will focus on the following nuclei: ¹⁷⁵Tl₉₆, ¹⁷⁷Tl₉₆, ¹⁷⁹Tl₉₈, ²¹¹Tl₁₃₀, ²¹³Tl₁₃₂, ¹⁸³Bi₁₀₀, ¹⁸⁵Bi₁₀₂, ²¹⁷Bi₁₃₄, ²¹⁹Bi₁₃₆, ¹⁹¹At₁₀₆, ¹⁹³At₁₀₈, ²¹⁹At₁₃₄, and ²²¹At₁₃₆. An interesting feature is that the levels at J^π = 1/2⁺, 7/2⁻, as well as 13/2⁺ decrease down to the ground level as the neutron numbers decrease in Bi and At nuclei. It is also interesting to expect to know whether the 7/2⁻ level would reach the ground state beyond N = 132 in the above nuclei. The shell migration of these orbitals is closely connected to the concepts of the triplet shape coexistence in the region of neutron deficient Pt, Os, Hg, and Pb.

The nuclei of interest can be investigated by the multi-transfer reactions at E ∼ 10 MeV per nucleon. For example the reaction of ¹³⁶Xe + ²⁰⁸Pb at E_cm = 526 Me is estimated to be 0.2 μb for the production of ²¹⁹At and 3 μb for the ²¹⁷Bi, respectively. However, the role of transfer channels is less clear due to the difficulty of making qualitative calculations for both the multi-nucleon transfer and the sub-barrier fusion simultaneously. The very neutron-rich RIBs, for example ¹⁴⁴Xe, with the high intensity and high quality with a few MeV per nucleon are essential for producing exotic nuclei far from the Z = 82 and N = 126 point, such as ¹⁹⁶Yb and ²²⁰Pt. It is noteworthy to mention that the measurements of half-lives of the nuclei with Z < 82 and N = 126 provide decisive information on the r-process paths along waiting points with N = 126, while the β-delayed neutron emission schemes in these neutron rich-nuclei play an important role in determining abundances of Au and Pt elements.

We have introduced and discussed the planned experiments using RIBs for the Korean Rare Isotope Beams Accelerator facility. This facility is one of the world-class multi-beam facilities capable of producing and accelerating beams of wide range mass of nuclides with energies of a few to hundreds MeV per nucleon. The low energy RIBs at E_lab = 5 to 20 MeV per nucleon are used for the study of nuclear structures and nuclear astrophysics toward and beyond the drip lines while the higher energy RIBs produced by the in-flight fragmentation with the reaccelerated ions from the ISOL enable us to explore the neutron drip lines in intermediate mass regions. Beam specifications for the KOBRA and ones for the IFFS spectrometers are complementary, which allow scientists to extent the investigations toward the very neutron-rich and proton-rich nuclei.

The experiments are planned to investigate the internal structures of exotic nuclei toward and beyond the nucleon drip lines by addressing the following questions: how the shell structure evolves in areas of extreme proton to neutron imbalance; whether the isospin symmetry maintains in isobaric mirror nuclei at and beyond the drip lines, how two-proton or two-neutron radioactivity affects abundances of the elements, what the role of the continuum states including resonant states above particle-decay threshold in exotic nuclei is in astrophysical nuclear reaction processes, and how the nuclear reaction rates triggered by unbound proton-rich nuclei make an effect on rapid proton capture processes in a very hot stellar plasma.

To summarize, we show a set of the planned experiments with the associated nuclei to be investigated over the nuclear mass chart in Fig. 32. In addition, we demonstrate the proposed, but rather challenging, experiments with the very intense and high quality RIBs in Fig. 33. We hope that the proposed experiments will play an important role in developing a concrete nuclear physics program for the rare isotope beams accelerator facilities, as well as in promoting the creation of next generation of nuclear scientists in the world.

Note 1. This paper has been made on the basis of the phenomenological arguments regarding the nuclear structures revealed in the systematics of the first 2⁺ levels of even-even nuclei and of the low-lying energy levels of odd-mass nuclei. Many references in the literatures related with the present work were not quoted because the referred data were almost taken from NNDC.

Note 2. The Rare Isotope Beams Accelerator Facility to be built in Korea has been named officially as ‘RAON’ which is said to mean ‘joyful, delightful’ in old Korean language.

This work was partially supported by the Rare Isotopes Science Project (RISP).