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Shell-model study on M1 strength distributions in N = 28 isotones
Volume 138B, number 1,2,3
PHYSICS LETTERS
12 April 1984
SHELL-MODEL S T U D Y ON M1 STRENGTH DISTRIBUTIONS IN N = 28 ISOTONES
K. MUTO and H. HORIE Department of Physics, Tokyo Institute of Technology, Oh.okayama, Meguro, Tokyo 152, Japan
Received 14 November 1983
Magnetic dipole excitations in N = 28 isotones 48Ca, S°Ti, S2Cr and 54Fe are studied in terms of shell model which includes configurations with one- and two-paiticle excitations from f7/2 to p 3/2, Pl/2 and f5/2 shell orbits. Distributions of the strength observed in (e, e') and (p, p') experiments are well reproduced. Total strength reduces by about 25% due to the mixing in the 0÷ ground state, but the calculated strengths are yet 2-3 times greater than the experimental values. Contributions arising from proton excitation and the orbital magnetization are also discussed.
In a backward-angle high-resolution (e, e') experiment, Eulenberg et al. [ 1] observed magnetic dipole excitations i n N = 2 isotones 48Ca, 50Ti, 52Cr and 54Fe. The electron scattering spectra are shown in fig. 1. In 48Ca, in addition to a 10.2 MeV state, which is very strongly excited in both (e, e') [2] and (p, p') [3 5] experiments, several states around 10.2 MeV are weakly excited. The spectrum of 50Ti(e, e') indicates fragmentation of the MI strength among five states with approximately equal magnitude and an additional state appears at 8.5 MeV. As one proceeds to 52Cr and 54Fe, higher fragmentation of strength is observed. Recently, Crawley reported [6] observation of magnetic dipole excitations in those nuclei in a proton inelastic scattering at Ep = 200 MeV. Energy distributions of the clustered peaks in the (p, p') spectra are in good agreement with those in the (e, e') experinaent. Eulenberg et al. [1 ] calculated ground-state M 1 transitions, using the effective interaction which was determined in a shell-model study on Fe isotopes [7] with a modification of single-particle energies. The calculations well account for the concentration of a significant amount of M1 strength in the energy region 9 - 1 0 . 5 MeV, but the observed fragmentation of strength cannot be reproduced in the model space which includes only one-particle excitation, f7/2 n + f7/2 n - 1(p3/2, Pl/2, f5/2) 1" In the case of 54Fe, they performed another calculation including twoparticle excitation and showed that the M1 strength 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
gets to be highly fragmented and the total strength below 11 MeV reduces by 15%. With respect to the total strength, experimentally deduced values are much smaller than the simple estimation which assumes f7/2 A 40 configuration for the 0 + ground state. The quenching of M 1 strength is partly explained by McGrory and Wildenthal [8] for Ca isotopes in ( f p ) A - 4 0 model calculations. We made the same calculations and found that destructive interference between f7/2 ~ f5/2 and f5/2 ~ f7/2 transition amplitudes reduces the total strength and therefore admixture o f f 7 / 2 A 42f5/22 configuration in the ground state is essential for the reduction [9]. We have carried out shell-model calculations of magnetic dipole excitations in N = 28 isotones 48Ca, 50Ti, 52Cr and 54Fe. Model space is constructed by the configurations on an inert 40Ca core f7/2 A - 4 0 - r e ( P 3 / 2 , Pl/2, f5/2) m with m = 0, 1 and 2. Single-particle energies and T = 1 matrix elements are taken from the work by McGrory and Wildenthal [8]. They modified the realistic interaction designed by Kuo and Brown [ 10] in order to reproduce low-lying energy spectra of Ca isotopes [11 ] and also excitation energy of the very strongly excited 1+ state in 48Ca [8]. As for T = 0 elements we adopt the modification suggested by Pasquini and Zuker [ 12], which shifts the monopole of inter-shell interaction
V o l u m e 138B, n u m b e r 1,2,3
PHYSICS L E T T E R S
12 A p r i l 1984
20
48Ca (e,e')
E0:30MeV
15
e
=165 °
10
E C r
5
U U 12
E lo ~c0~ u
1
5°Ti (e,e')
8 6
14
52
!~
Cr (e,e')
8 14
l
R
~;
g.o
a:s
i
9.0
i
9.s Excitation
i
10.0
l&~
54
Fe (e,e')
1~.0
11.5'
~£o
EnergylMeV
Fig. l . H i g h - r e s o l u t i o n inelastic e l e c t r o n s c a t t e r i n g spectra o f the N = 28 i s o t o n e s , t a k e n f r o m ref. [ 1 ]. The s t r o n g e s t m a g n e t i c dip o l e t r a n s i t i o n s are i n d i c a t e d b y arrows.
diagonalizing the model hamiltonian and the groundstate M1 transitions are calculated for all 1+ states with T = T O and T = T O + 1, where T O = ( N - Z ) / 2 is groundstate isospin. Fig. 2 shows distributions o f magnetic dipole strength calculated with the free-nucleon g factors. The very strongly excited 1 + state o f 48Ca is reproduced at 10.4 MeV and B(M1) = 8.0/22 to this state exhausts 94% of theoretical total strength. The remaining small fraction is shared by several states as observed in the (e, e ' ) measurement [1]. In other nuclei M1 strength, in particular T = T o component, is calculated to be highly fragmented and agreement with experiment becomes much better than that o f calculations which include only one-particle excitation. In 50Ti, an 8.5 MeV state and a cluster o f strength 10
around I0.4 MeV would correspond to the peaks ob, served at 8.5 MeV and 10.2 MeV [ 1,6], respectively. The present calculation predicts another state with large strength at 6.6 MeV, which is located outside the energy region in which the (e, e ' ) m e a s u r e m e n t was made [1] and was not identified in the (p, p ' ) experiment [6]. The T = 4 component might be too small to be detected experimentally. In 52Cr, calculated strength distributes in a number o f T = 2 states in a broad energy range 7 12 MeV and each state has a small fraction o f strength. The distribution seems in fairly good agreement with the experimental data. The calculation does not suggest noticeable strength to T = 3 states. In 54Fe, calculation well accounts for the concentration o f strength to T = 1 states between 8.8- 1 0 . 0 MeV. However, it is noted that about I/4 of the
Volume 138B, number 1,2,3
PHYSICS LETTERS ,
8
,
,
,
[
48Ca
7 6
5 4 3 2 1
0
I
5OTi
2 1
3
eqZ
..~
'
'l
0
' "
,
I
.
_
I.[-.
I
'
L
' -'
0
'
I
52Cr
2
•
~-~ •-
3
::E
2
1 I
0
,, ,
,if.
,
[
54Fe
i
. . . .
I
0
I
I I
3
,
2 0
I ......
2
0
. i
6
I
'
'
7
8
,IJll -i
I
1!
. . . .
I
9 10 11 12 13 14 15 16 17
Ex
MeV
Fig. 2. Distributions of ground-state magnetic dipole transitions in 48Ca, 5°Ti, s2 Cr and s4 Fe calculated with free-nucleon g factors. Isospin components with T = To (lower part) and T = To + 1 (upper part) are separately shown for each nucleus. T = 1 component is scattered in many states above I0 MeV. The 54Fe is the only nucleus o f those under consideration in which excitation of T = T O + 1 1+ states is experimentally confirmed [ 1 ]. Two states observed at 10.5 MeV and 1 1 .I MeV are reproduced in the present calculation. Contributions of proton and neutron transitions are separately calculated and interference between them is investigated. Proton transition gives rise to large strength in a few states below 8 MeV, but it interferes destructively with neutron transition to result in small B(M1) values to those low-lying states. Only one exception is the 6.6 MeV state in 5°Ti, in which proton excitation is exclusively dominant. On the other hand, neutron transition dominates above 8 MeV and enhance-
12 April 1984
s e n t o f M 1 strength around 10 MeV is obtained by associating constructive interference with small contribution o f proton transition. No substantial effects o f orbital magnetization are found. Strength due to the orbital part of the magnetic dipole transition operator is distributed over a number of states in a wide energy region and it sums up at most l / l 2. In the neutron-shell closed N = 28 isotones, magnetic dipole excitation is dominated by a spin-flip transition from f7/2 to f5/2, and in the single-particle matrix element (f5 / 2 [[M 1 [! f7 / 2) the orbital component is much smaller than the spin component. It is noted, however, since both components have comparable magnitudes in transitions without spin-flip, the orbital part may play an important role in those nuclei in which neither proton nor neutron shells are closed. Kniipfer and Metsch pointed out the importance of the orbital magnetization in 20Ne [ 13]. Calculated total strength and its reduction due to the ground-state configuration mixing are listed in table l. The reduction factor is defined by a ratio o f the total strength over the single-particle limit which assumes f7/2 A 40 configuration for the 0 + ground state and free-nucleon g factors. The T = T O component reduces by 2 0 % - 3 0 % approximately independent of the nucleus, while further reduction which depends on mass number is obtained for the T = T O + 1 component. The theoretical total strengths, however, are larger by a factor of 2 - 3 than experimental values, 4.6 -+ 0.5/12, 3.4 -+ 0.4/12N, 5.0 + 0.5 /~2 and 6.3 + 0.6 # 2 for 48Ca, 50Ti ' 52Cr and 54Fe, respectively [11. In the model space with only 0?~w excitations, fects of higher configuration mixing on magnetic dipole transitions could be taken into account by renorrealization o f g factors. Shimizu et al. [14] carried out perturbative calculations on magnetic moments in nuclei with an LS-closed core plus or minus one nucleon and showed that deviation from the Schmidt value is explained mainly by admixture of a number of configurations with high excitation in the wavefunction. We therefore adopt effective spin g factors which reproduce observed magnetic moments of 7 / 2 ground states o f 41Ca and 41Sc L[~lJq l ~ ogproton = S + 4.88/~N and g~seutr°n = - 3 . 1 9 / ~ N , assuming gproton = 1 /~N and g~Qeutron = 0. In comparison with the results with free-nucleon g factors, the renormalization little affects distributions of strength except overall hindrance, since it reduces proton and neutron 11
Volume 138B, number 1,2,3
PHYSICS LETTERS
] 2 April 1984
Table 1 2 Total strength (in tLN) , reduction factor compared with the single-particlelimit and centroid energy (in MeV) of ground-state M1 transitions in 48Ca, 5°Ti, S2Cr and 54Fe. The T = To and To + 1 components are separately given. Calculations are made with freenucleon g factors and with the renormalized ones (see text). Nucleus
Total strength
Reduction factor
To
To+I
To
T0+I
To
T0+I
free nucleon g factors
48Ca 5°Ti 52Cr S4Fe
8.56 11.72 12.57 10.76
0.36 1.89 5.69
0.71 0.81 0.80 0.77
0.20 0.39 0.52
10.46 9.92 10.18 10.26
14.96 12.60 11.61
normalised g factors
48Ca so Ti 52Cr 54Fe
5.93 8.47 9.12 7.81
0.23 1.29 4.01
0.49 0.58 0.58 0.56
0.13 0.27 0.37
10.46 9.90 10.20 10.31
15.38 12.66 11.67
spin-flip transitions almost equally. The total strengths and reduction factors are also presented in table 1. Agreement with experimental values is much improved though significant disagreement still exists in 50Ti, 52Cr and 54Fe. With respect to the experimentally deduced strength, it should be noted that the total strength observed in 50Ti is smaller than that in 48Ca. In 50Ti one could expect additional strength arising from excitation of protons. Centroid energies of T O and T O + 1 components are evaluated and are shown in table 1. Isospin splittings in the present calculation are generally larger than those obtained in the shell-model calculation by Eulenberg et al. [ 1]. The discrepancy should be attributed to difference of model hamiltonian. Both theoretical estimations, however, do not follow the relation V I ( T 0 + 1)/A with V1 = 85 MeV which was suggested by Sterrenburg et al. [ 16] in the analysis of energy systematics of observed M1 excitations in heavy nuclei. In summary, we have studied distributions of ground state magnetic dipole transitions in N = 28 isotones, 48Ca, 50Ti, 52Cr and 54 Fe. Shell-model calculations which include one- and two-particle excitations well account for the fragmented strength distributions observed in electron and proton inelastic scattering experiments. In 50Ti, 52Cr and 54Fe, at lower excitation energy, proton excitation makes appreciable contributions although destructively interfering with neutron excitation, whereas constructive coherence between proton and neutron transitions enhances magnetic dipole strength around 10 MeV. Due to the 12
Centroid energy
ground-state configuration mixing total strength reduces by about 25%. Moreoever, introducing effective g factors which reproduce magnetic moments of 7 / 2 - ground states of 41Ca and 41Sc, we obtain about 50% reduction. The numerical calculations were made by using the HITAC M-280 computer system at the Tokyo Institute of Technology. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [ 11 ] [12] [13] [14] [15] [ 16 ]
G. Eulenberg et al., Phys. Lett. 116B (1982) 113. W. Steffen et al., Phys. Lett. 95B (1980) 23. Y. Fujita et al., Phys. Rev. C25 (1982) 678. G.P.A. Berg et al., Phys. Rev. C25 (1982) 2100. G.M. Crawley et al., Phys. Lett. 127B (1983) 322. G.M. Crawley, in: Proc. Intern. Syrup. on Light ion reaction mechanism (Osaka, 1983), to be published. R. Vennink and P.W.M. Glaudemans, Z. Phys. A294 (1980) 241. J.B. McGrory and B.H. Wildenthal, Phys. Lett. 103B (1981) 173. K. Muto and H. Horie, unpublished. T.T.S. Kuo and G.E. Brown, Nucl. Phys. All4 (1968) 241. J.B. McGrory, B.H. Wildenthal and E.H. Halbert, Phys. Rev. C2 (1970) 186. E. Pasquini and A. Zuker, in: Proc. Topical Conf. on Physics of medium light nuclei (Firenze, 1977), p. 62. W. Kntipfer and B.C. Metsch, Phys. Rev. C27 (1983) 2487. K. Shimizu, M. Ichimura and A. Arima, Nucl. Phys. A226 (1974) 282. P.M. Endt and C. Van der Leun, Nucl. Phys. A310 (1978) 1. W.A.Sterrenburg, S.M. Austin, R.P. DeVito and A. Galonsky, Phys. Rev. Lett. 45 (1980) 1839.
PHYSICS LETTERS
12 April 1984
SHELL-MODEL S T U D Y ON M1 STRENGTH DISTRIBUTIONS IN N = 28 ISOTONES
K. MUTO and H. HORIE Department of Physics, Tokyo Institute of Technology, Oh.okayama, Meguro, Tokyo 152, Japan
Received 14 November 1983
Magnetic dipole excitations in N = 28 isotones 48Ca, S°Ti, S2Cr and 54Fe are studied in terms of shell model which includes configurations with one- and two-paiticle excitations from f7/2 to p 3/2, Pl/2 and f5/2 shell orbits. Distributions of the strength observed in (e, e') and (p, p') experiments are well reproduced. Total strength reduces by about 25% due to the mixing in the 0÷ ground state, but the calculated strengths are yet 2-3 times greater than the experimental values. Contributions arising from proton excitation and the orbital magnetization are also discussed.
In a backward-angle high-resolution (e, e') experiment, Eulenberg et al. [ 1] observed magnetic dipole excitations i n N = 2 isotones 48Ca, 50Ti, 52Cr and 54Fe. The electron scattering spectra are shown in fig. 1. In 48Ca, in addition to a 10.2 MeV state, which is very strongly excited in both (e, e') [2] and (p, p') [3 5] experiments, several states around 10.2 MeV are weakly excited. The spectrum of 50Ti(e, e') indicates fragmentation of the MI strength among five states with approximately equal magnitude and an additional state appears at 8.5 MeV. As one proceeds to 52Cr and 54Fe, higher fragmentation of strength is observed. Recently, Crawley reported [6] observation of magnetic dipole excitations in those nuclei in a proton inelastic scattering at Ep = 200 MeV. Energy distributions of the clustered peaks in the (p, p') spectra are in good agreement with those in the (e, e') experinaent. Eulenberg et al. [1 ] calculated ground-state M 1 transitions, using the effective interaction which was determined in a shell-model study on Fe isotopes [7] with a modification of single-particle energies. The calculations well account for the concentration of a significant amount of M1 strength in the energy region 9 - 1 0 . 5 MeV, but the observed fragmentation of strength cannot be reproduced in the model space which includes only one-particle excitation, f7/2 n + f7/2 n - 1(p3/2, Pl/2, f5/2) 1" In the case of 54Fe, they performed another calculation including twoparticle excitation and showed that the M1 strength 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
gets to be highly fragmented and the total strength below 11 MeV reduces by 15%. With respect to the total strength, experimentally deduced values are much smaller than the simple estimation which assumes f7/2 A 40 configuration for the 0 + ground state. The quenching of M 1 strength is partly explained by McGrory and Wildenthal [8] for Ca isotopes in ( f p ) A - 4 0 model calculations. We made the same calculations and found that destructive interference between f7/2 ~ f5/2 and f5/2 ~ f7/2 transition amplitudes reduces the total strength and therefore admixture o f f 7 / 2 A 42f5/22 configuration in the ground state is essential for the reduction [9]. We have carried out shell-model calculations of magnetic dipole excitations in N = 28 isotones 48Ca, 50Ti, 52Cr and 54Fe. Model space is constructed by the configurations on an inert 40Ca core f7/2 A - 4 0 - r e ( P 3 / 2 , Pl/2, f5/2) m with m = 0, 1 and 2. Single-particle energies and T = 1 matrix elements are taken from the work by McGrory and Wildenthal [8]. They modified the realistic interaction designed by Kuo and Brown [ 10] in order to reproduce low-lying energy spectra of Ca isotopes [11 ] and also excitation energy of the very strongly excited 1+ state in 48Ca [8]. As for T = 0 elements we adopt the modification suggested by Pasquini and Zuker [ 12], which shifts the monopole of inter-shell interaction
V o l u m e 138B, n u m b e r 1,2,3
PHYSICS L E T T E R S
12 A p r i l 1984
20
48Ca (e,e')
E0:30MeV
15
e
=165 °
10
E C r
5
U U 12
E lo ~c0~ u
1
5°Ti (e,e')
8 6
14
52
!~
Cr (e,e')
8 14
l
R
~;
g.o
a:s
i
9.0
i
9.s Excitation
i
10.0
l&~
54
Fe (e,e')
1~.0
11.5'
~£o
EnergylMeV
Fig. l . H i g h - r e s o l u t i o n inelastic e l e c t r o n s c a t t e r i n g spectra o f the N = 28 i s o t o n e s , t a k e n f r o m ref. [ 1 ]. The s t r o n g e s t m a g n e t i c dip o l e t r a n s i t i o n s are i n d i c a t e d b y arrows.
diagonalizing the model hamiltonian and the groundstate M1 transitions are calculated for all 1+ states with T = T O and T = T O + 1, where T O = ( N - Z ) / 2 is groundstate isospin. Fig. 2 shows distributions o f magnetic dipole strength calculated with the free-nucleon g factors. The very strongly excited 1 + state o f 48Ca is reproduced at 10.4 MeV and B(M1) = 8.0/22 to this state exhausts 94% of theoretical total strength. The remaining small fraction is shared by several states as observed in the (e, e ' ) measurement [1]. In other nuclei M1 strength, in particular T = T o component, is calculated to be highly fragmented and agreement with experiment becomes much better than that o f calculations which include only one-particle excitation. In 50Ti, an 8.5 MeV state and a cluster o f strength 10
around I0.4 MeV would correspond to the peaks ob, served at 8.5 MeV and 10.2 MeV [ 1,6], respectively. The present calculation predicts another state with large strength at 6.6 MeV, which is located outside the energy region in which the (e, e ' ) m e a s u r e m e n t was made [1] and was not identified in the (p, p ' ) experiment [6]. The T = 4 component might be too small to be detected experimentally. In 52Cr, calculated strength distributes in a number o f T = 2 states in a broad energy range 7 12 MeV and each state has a small fraction o f strength. The distribution seems in fairly good agreement with the experimental data. The calculation does not suggest noticeable strength to T = 3 states. In 54Fe, calculation well accounts for the concentration o f strength to T = 1 states between 8.8- 1 0 . 0 MeV. However, it is noted that about I/4 of the
Volume 138B, number 1,2,3
PHYSICS LETTERS ,
8
,
,
,
[
48Ca
7 6
5 4 3 2 1
0
I
5OTi
2 1
3
eqZ
..~
'
'l
0
' "
,
I
.
_
I.[-.
I
'
L
' -'
0
'
I
52Cr
2
•
~-~ •-
3
::E
2
1 I
0
,, ,
,if.
,
[
54Fe
i
. . . .
I
0
I
I I
3
,
2 0
I ......
2
0
. i
6
I
'
'
7
8
,IJll -i
I
1!
. . . .
I
9 10 11 12 13 14 15 16 17
Ex
MeV
Fig. 2. Distributions of ground-state magnetic dipole transitions in 48Ca, 5°Ti, s2 Cr and s4 Fe calculated with free-nucleon g factors. Isospin components with T = To (lower part) and T = To + 1 (upper part) are separately shown for each nucleus. T = 1 component is scattered in many states above I0 MeV. The 54Fe is the only nucleus o f those under consideration in which excitation of T = T O + 1 1+ states is experimentally confirmed [ 1 ]. Two states observed at 10.5 MeV and 1 1 .I MeV are reproduced in the present calculation. Contributions of proton and neutron transitions are separately calculated and interference between them is investigated. Proton transition gives rise to large strength in a few states below 8 MeV, but it interferes destructively with neutron transition to result in small B(M1) values to those low-lying states. Only one exception is the 6.6 MeV state in 5°Ti, in which proton excitation is exclusively dominant. On the other hand, neutron transition dominates above 8 MeV and enhance-
12 April 1984
s e n t o f M 1 strength around 10 MeV is obtained by associating constructive interference with small contribution o f proton transition. No substantial effects o f orbital magnetization are found. Strength due to the orbital part of the magnetic dipole transition operator is distributed over a number of states in a wide energy region and it sums up at most l / l 2. In the neutron-shell closed N = 28 isotones, magnetic dipole excitation is dominated by a spin-flip transition from f7/2 to f5/2, and in the single-particle matrix element (f5 / 2 [[M 1 [! f7 / 2) the orbital component is much smaller than the spin component. It is noted, however, since both components have comparable magnitudes in transitions without spin-flip, the orbital part may play an important role in those nuclei in which neither proton nor neutron shells are closed. Kniipfer and Metsch pointed out the importance of the orbital magnetization in 20Ne [ 13]. Calculated total strength and its reduction due to the ground-state configuration mixing are listed in table l. The reduction factor is defined by a ratio o f the total strength over the single-particle limit which assumes f7/2 A 40 configuration for the 0 + ground state and free-nucleon g factors. The T = T O component reduces by 2 0 % - 3 0 % approximately independent of the nucleus, while further reduction which depends on mass number is obtained for the T = T O + 1 component. The theoretical total strengths, however, are larger by a factor of 2 - 3 than experimental values, 4.6 -+ 0.5/12, 3.4 -+ 0.4/12N, 5.0 + 0.5 /~2 and 6.3 + 0.6 # 2 for 48Ca, 50Ti ' 52Cr and 54Fe, respectively [11. In the model space with only 0?~w excitations, fects of higher configuration mixing on magnetic dipole transitions could be taken into account by renorrealization o f g factors. Shimizu et al. [14] carried out perturbative calculations on magnetic moments in nuclei with an LS-closed core plus or minus one nucleon and showed that deviation from the Schmidt value is explained mainly by admixture of a number of configurations with high excitation in the wavefunction. We therefore adopt effective spin g factors which reproduce observed magnetic moments of 7 / 2 ground states o f 41Ca and 41Sc L[~lJq l ~ ogproton = S + 4.88/~N and g~seutr°n = - 3 . 1 9 / ~ N , assuming gproton = 1 /~N and g~Qeutron = 0. In comparison with the results with free-nucleon g factors, the renormalization little affects distributions of strength except overall hindrance, since it reduces proton and neutron 11
Volume 138B, number 1,2,3
PHYSICS LETTERS
] 2 April 1984
Table 1 2 Total strength (in tLN) , reduction factor compared with the single-particlelimit and centroid energy (in MeV) of ground-state M1 transitions in 48Ca, 5°Ti, S2Cr and 54Fe. The T = To and To + 1 components are separately given. Calculations are made with freenucleon g factors and with the renormalized ones (see text). Nucleus
Total strength
Reduction factor
To
To+I
To
T0+I
To
T0+I
free nucleon g factors
48Ca 5°Ti 52Cr S4Fe
8.56 11.72 12.57 10.76
0.36 1.89 5.69
0.71 0.81 0.80 0.77
0.20 0.39 0.52
10.46 9.92 10.18 10.26
14.96 12.60 11.61
normalised g factors
48Ca so Ti 52Cr 54Fe
5.93 8.47 9.12 7.81
0.23 1.29 4.01
0.49 0.58 0.58 0.56
0.13 0.27 0.37
10.46 9.90 10.20 10.31
15.38 12.66 11.67
spin-flip transitions almost equally. The total strengths and reduction factors are also presented in table 1. Agreement with experimental values is much improved though significant disagreement still exists in 50Ti, 52Cr and 54Fe. With respect to the experimentally deduced strength, it should be noted that the total strength observed in 50Ti is smaller than that in 48Ca. In 50Ti one could expect additional strength arising from excitation of protons. Centroid energies of T O and T O + 1 components are evaluated and are shown in table 1. Isospin splittings in the present calculation are generally larger than those obtained in the shell-model calculation by Eulenberg et al. [ 1]. The discrepancy should be attributed to difference of model hamiltonian. Both theoretical estimations, however, do not follow the relation V I ( T 0 + 1)/A with V1 = 85 MeV which was suggested by Sterrenburg et al. [ 16] in the analysis of energy systematics of observed M1 excitations in heavy nuclei. In summary, we have studied distributions of ground state magnetic dipole transitions in N = 28 isotones, 48Ca, 50Ti, 52Cr and 54 Fe. Shell-model calculations which include one- and two-particle excitations well account for the fragmented strength distributions observed in electron and proton inelastic scattering experiments. In 50Ti, 52Cr and 54Fe, at lower excitation energy, proton excitation makes appreciable contributions although destructively interfering with neutron excitation, whereas constructive coherence between proton and neutron transitions enhances magnetic dipole strength around 10 MeV. Due to the 12
Centroid energy
ground-state configuration mixing total strength reduces by about 25%. Moreoever, introducing effective g factors which reproduce magnetic moments of 7 / 2 - ground states of 41Ca and 41Sc, we obtain about 50% reduction. The numerical calculations were made by using the HITAC M-280 computer system at the Tokyo Institute of Technology. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [ 11 ] [12] [13] [14] [15] [ 16 ]
G. Eulenberg et al., Phys. Lett. 116B (1982) 113. W. Steffen et al., Phys. Lett. 95B (1980) 23. Y. Fujita et al., Phys. Rev. C25 (1982) 678. G.P.A. Berg et al., Phys. Rev. C25 (1982) 2100. G.M. Crawley et al., Phys. Lett. 127B (1983) 322. G.M. Crawley, in: Proc. Intern. Syrup. on Light ion reaction mechanism (Osaka, 1983), to be published. R. Vennink and P.W.M. Glaudemans, Z. Phys. A294 (1980) 241. J.B. McGrory and B.H. Wildenthal, Phys. Lett. 103B (1981) 173. K. Muto and H. Horie, unpublished. T.T.S. Kuo and G.E. Brown, Nucl. Phys. All4 (1968) 241. J.B. McGrory, B.H. Wildenthal and E.H. Halbert, Phys. Rev. C2 (1970) 186. E. Pasquini and A. Zuker, in: Proc. Topical Conf. on Physics of medium light nuclei (Firenze, 1977), p. 62. W. Kntipfer and B.C. Metsch, Phys. Rev. C27 (1983) 2487. K. Shimizu, M. Ichimura and A. Arima, Nucl. Phys. A226 (1974) 282. P.M. Endt and C. Van der Leun, Nucl. Phys. A310 (1978) 1. W.A.Sterrenburg, S.M. Austin, R.P. DeVito and A. Galonsky, Phys. Rev. Lett. 45 (1980) 1839.