Analogous Gamow-Teller and M 1 transitions in
26
Mg,
26
Al, and
26
Si
Y. Fujita,
1,
* Y. Shimbara,
1
A. F. Lisetskiy,
2,†
T. Adachi,
1
G. P. A. Berg,
3,‡
P. von Brentano,
2
H. Fujimura,
3
H. Fujita,
1,§
K. Hatanaka,
3
J. Kamiya,
3
T. Kawabata,
3,
H. Nakada,
4
K. Nakanishi,
3
Y. Shimizu,
3
M. Uchida,
5
and M. Yosoi
5
1
Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan
2
Institut fu ¨r Kernphysik, Universita ¨t zu Ko ¨ln, 50937 Ko ¨ln, Germany
3
Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan
4
Department of Physics, Chiba University, Inage, Chiba 263-8522, Japan
5
Department of Physics, Kyoto University, Kyoto 606-8502, Japan
Received 29 January 2003; published 25 June 2003
Under the assumption that isospin T is a good quantum number, isobaric analog states and various analogous
transitions among these states are expected in isobars with mass number A. Strengths of analogous Gamow-
Teller GT and M 1 transitions have been compared for an A =26 isobar triplet with T
z
=+1, 0, and -1,
where T
z
is defined by T
z
=( N -Z )/2. The T
z
=+1 →0 GT transitions from the J
=0
+
ground state of
26
Mg
to excited J
=1
+
states in
26
Al were studied up to the excitation energy ( E
x
) of 9 MeV by using a high
energy-resolution (
3
He, t ) reaction. The distribution of observed GT strengths was well reproduced in a shell-
model calculation. The isospin symmetric T
z
=-1 →0 GT transitions can be studied in the
26
Si decay. The
GT strengths from the (
3
He, t ) reaction were in good agreement with the -decay values evaluated up to E
x
=2.7-MeV states in
26
Al. The GT strengths were further compared with the strengths of analogous M 1
transitions in
26
Al, i.e., the M 1 transitions from the excited 1
+
states to the isobaric analog state of the
26
Mg
ground state in
26
Al. Through this comparison, contributions of spin and orbital terms in these M 1 transitions
were studied. The GT and M 1 strengths as well as spin and orbital contributions in M 1 strengths are inter-
preted by both the shell model and the particle-rotor model assuming a correlated proton and neutron pair
around a
24
Mg core. The isospin T of each excited 1
+
state in
26
Al was also studied by examining the
existence or the nonexistence of the analog 1
+
state in the T
z
=1
26
Mg nucleus.
DOI: 10.1103/PhysRevC.67.064312 PACS numbers: 25.55.Kr, 21.10.Hw, 23.20.Lv, 27.30.+t
I. INTRODUCTION
Isospin is a good quantum number under the assumption
that the nuclear interaction is charge symmetric and that the
effect of the electromagnetic interaction is relatively small.
As such, an analogous structure is expected for the same
mass A nuclei with different T
z
, where T
z
=( N -Z )/2 is
the z component of the isospin T see e.g., Refs. 1,2. The
corresponding states in different T
z
nuclei isobars are
called isobaric analog states or simply analog states. Tran-
sitions connecting various combinations of analog states are
also analogous. Such ‘‘analogous transitions’’ should have
corresponding energies and strengths. Aspects and properties
of analogous transitions in isobars have been discussed ex-
tensively in Refs. 1,3. Through the identification of analo-
gous transitions and the systematics of excitation energies,
isospin values of excited states have been determined. The
analog states for various isobars, and thus the isospin sym-
metry of isobars, are listed in Ref. 4 for sd -shell nuclei.
In order to study the analog states and the properties of
analogous transitions in isobars, we select simple transitions
caused mainly by the spin-isospin ( ) operator, i.e.,
Gamow-Teller GT and M 1 transitions.
The GT transitions, caused purely by the -type opera-
tor, are well suited for this purpose, because they can be
studied in both decays and hadron charge-exchange CE
reactions. The GT transitions are characterized by L =0,
S =1, and T
z
=1, where L and S are the orbital and
spin quantum numbers. An important physical quantity for
understanding the nuclear structure is the reduced GT transi-
tion strength B (GT). The most direct information on B (GT)
values is obtained from studies of GT decay. In addition,
CE reactions, such as ( p , n ) or (
3
He, t ), performed at inter-
mediate energies ( 100 MeV/nucleon) can be used as a
means to map the GT strengths over a wide range of excita-
tion energy ( E
x
) 5,6. For this purpose, one relies upon the
approximate proportionality between the reaction cross sec-
tions measured at the scattering angle =0° and the B (GT)
values 7.
The magnetic dipole ( M 1) operator for M 1 transitions
is similar to the GT operator in that its major component is
the isovector IV spin ( ) term 8–10. The main differ-
ence between them is that the electromagnetic M 1 operator
contains not only the term, but also IV orbital ( ),
isoscalar IS spin ( ), and IS orbital ( ) terms. These ad-
ditional terms can interfere with the term constructively
or destructively. Another difference is that the M 1 operator
has a T
z
=0 nature. The most direct information on the
*Electronic address: fujita@rcnp.osaka-u.ac.jp
†
Present address: NSCL, Michigan State University, East Lansing,
MI 48824.
‡
Present address: KVI, Zernikelaan 25, 9747 AA Groningen, The
Netherlands.
§
Present address: Research Center for Nuclear Physics, Osaka
University, Ibaraki, Osaka 567-0047, Japan.
Present address: CNS, University of Tokyo in RIKEN campus,
Wako, Saitama 351-0198, Japan.
PHYSICAL REVIEW C 67, 064312 2003
0556-2813/2003/676/06431212/$20.00 ©2003 The American Physical Society 67 064312-1