Using the one-dimensional potential well with realistic parameters for atomic nuclei, we illustrate the movement of the poles of the S-matrix and the transmission coefficient when the well supports an anti-bound state. We calculate the phase shift of the atomic nuclei 5He using the three-dimensional potential well and compare it with the experimental one. The paper gives an introduction to some of the properties found in realistic loosely bound and resonant nuclear systems, using mathematics accessible to undergraduate students.
REFERENCES
1.
V. I.
Kukulin
,
V. M.
Krasnopol'sky
, and
J.
Horáček
, Theory of Resonances: Principles and Applications
(
Springer
,
Netherlands
, 1989
).2.
C. L.
Hammer
,
T. A.
Weber
, and
V. S.
Zidell
, “
Time-dependent scattering of wave packets in one dimension
,” Am. J. Phys.
45
, 933
–941
(1977
).3.
M.
Staelens
and
F.
Marsiglio
, “
Scattering problems via real-time wave packet scattering
,” arXiv:2103.01027 (2021
).4.
Roger G.
Newton
, Scattering Theory of Waves and Particles
(
Springer
,
New York
, 1982
).5.
D. G.
Zill
and
P. D.
Shanahan
, Complex Analysis with Applications
(
Jones and Bartlett Learning
,
Boston
, 2015
).6.
H. C.
Ohanian
and
C. G.
Ginsburg
, “
Antibound ‘states’ and resonances
,” Am. J. Phys.
42
, 310
–315
(1974
).7.
A.
Bohm
,
M.
Gadella
, and
G.
Bruce Mailand
, “
Gamow vectors and decaying states
,” Am. J. Phys.
57
, 1103–1108
(1989
).8.
A.
Moroz
and
A. E.
Miroshnichenko
, “
On beautiful analytic structure of the s-matrix
,” New J. Phys.
21
, 103035
(2019
).9.
M.
Abramowitz
and
I. A.
Stegun
, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
(
Dover
,
New York
, 1964
).10.
R. G.
Newton
, Quantum Physics. A Text for Graduate Students
(
Springer
,
New York
, 2002
).11.
C.
Cohen-Tannoudji
,
B.
Diu
, and
F.
Laloe
, Quantum Mechanics
(
Wiley-VCH
,
New York
, 1991
).12.
D. W. L.
Sprung
,
H.
Wu
, and
J.
Martorell
, “
Poles, bound states, and resonances illustrated by the square well potential
,” Am. J. Phys.
64
, 136
–144
(1996
).13.
A. U.
Maheswari
,
P.
Prema
, and
C. S.
Shastry
, “
Resonant states and transmission coefficient oscillations for potential wells and barriers
,” Am. J. Phys.
78
, 412
–417
(2010
).14.
Z.
Ahmed
, “
Comment on ‘Resonant states and transmission coefficient oscillations for potential wells and barriers,’ by A. Uma Maheswari, P. Prema, and C. S. Shastry [Am. J. Phys. 78 (4), 412–417 (2010)]
,” Am. J. Phys.
79
, 682
–683
(2011
).15.
C. A.
Bertulani
, Nuclear Physics in a Nutshell
(
Princeton U. P
.,
Princeton
, 2007
).16.
See https://www.nndc.bnl.gov/nudat2/getdatasetClassic.jsp?nucleus=2H&unc=nds for “Brookhaven National Laboratory National Nuclear Data Center, NUDAT (Nuclear Structure and Decay Data).”
17.
J.
Bond
and
F.
Firk
, “
Determination of R-function and physical-state parameters for n-4He elastic scattering below 21 MeV
,” Nucl. Phys. A
287
, 317
–343
(1977
).18.
© 2022 Author(s). Published under an exclusive license by American Association of Physics Teachers.
2022
Author(s)
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
