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Spin assignments in Mn55 via inelastic neutron scattering
Volume 4, number 4
PHYSICS
LETTERS
The authors wish to thank Dr. C. A. Heras for a stimulating discussion.
3) 0. M. Bilaniuk and R. J. Slobodrian, to be published. 4) J.S. Blair, Phys. Rev. 115 (1959) 928, and references therein. 5) J.S. Blair, Proc. of the Int. Conf. on Nuclear Structure, Kingston, Canada (University of Toronto Press, Toronto, 1960) p. 827. 6) M.A.Preston, Physics of the nucleus (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962) Chapter 19. 7) Ray Satchler, private communication.
1) C.R. Lubitz, Numerical tables of Butler-Born approximation stripping cross sections (University of Michigan, Ann Arbor, Michigan, 1957), unpublished. 2) Vera Kistiakowsky-Fischer, Bull. Am. Phys. Sot. 2 (1957) 28.
SPIN
ASSIGNMENTS
IN Mn55
VIA
15 April 1963
INELASTIC
NEUTRON
SCATTERING
R. C. LAMB * and M. T. McELLISTREM University of Kentucky, Lexington, Kentucky ** Received 21 March 1963
The purpose of this letter is to present evidence for a definite spin sequence for the first three excited levels of Mn55 and for a tentative assignment for the fourth. These levels are located at 0.126, 0.983, 1.289 and 1.527 MeV. The basis for these assignments is a recently concluded series of measurements of inelastic neutron scattering 1). Recently published work, both experimental and theoretical, has indicated interest in but uncertainty about the spin assignments for the excited levels of Mn55. Previous spectroscopic work on the lowlying levels of Mn55 is summarised in the following four paragraphs. 1. A coulomb excitation study of the 0.126 MeV level had resulted in an assignment of i- for that level 2). However, a more recent study of this state has indicated that an assignment of s- or zis consistent with Coulomb excitation measurements 3). 2. Nath et al. have measured gamma ray production cross sections and level-decay branching ratios 4) for neutron energies between 1.2 MeV and 2.47 MeV. On the basis of their measurements, earlier scattering studies, and shell model expectations they suggested a spin sequence of $, 7 and $ for the second, third and fourth levels respectively. 3. Calculations presented in other work 5) on inelastic scattering in Mn55 have indicated a slight preference for a i assignment for the second excited state at 0.983 MeV rather than the tentative 5 assignment of Nath et al. 4. Finally, in a recent shell-model calculation 6) * National Science Foundation pre-doctoral
Fellow 1959-61. ** This work was partially supported by the United States Atomic Energy Commission.
of the level structure of Mn55 the spin and parity of the second excited state has been assumed to be i- in contrast to the 4 suggestion of Nath et al. The spin assignments presented in this letter are an effort to clarify the situation for the lowlying levels of Mn55. The use of inelastic neutron scattering as a spectroscopic tool depends on two principal assumptions. The first states that the neutron-nucleus interaction can be represented by a potential. The second is a conclusion of the statistical model, that the mode of decay of the compound system (n + target) is independent of its mode of formation. The potentials used to represent neutron inelastic scattering measurements have been those determined to fit the average dependence of total and elastic scattering cross sections as a function of energy and atomic weight. This representation has correctly discriminated between strong and weakly excited transitions, but good quantitative agreement between model calculations and measurements to individual final states has not been a general result. Hence the uncertainty in the interpretation of past inelastic scattering studies in Mn55. The study which is the basis for this letter includes a modified model for the calculation of the theoretical cross sections. The two assumptions mentioned above are retained, but the neutron-nucleus potential has been adjusted to force a fit to measured non-elastic cross sections and differential elastic cross sections 7) for the nucleus under study. With this model, the excitation of several states in each of the nuclei A127, Mn55 and Fe56 have been represented to well within the uncertainties on the measurements l). A result has been the spin and parity assignments reported here. Measured differential gamma ray production 211
Volume 4, number 4
PHYSICS
cross sections and decay branching ratios 1) yield the total inelastic scattering cross sections shown in table 1. The neutron bombarding energy was chosen as 2.21 MeV, since the Mn55 levels are easily resolved below that energy. The uncertainties shown are relative uncertainties, and an additional systematic uncertainty of vo is attributed to the magnitudes. Table 1 also contains several cross section ratios, with uncertainties, since Table 1 Measured and calculated neutron inelastic scattering cross sections in Mn55 for a neutron energy of 2.21 MeV. Also included are measured cross section ratios. The spin and parity assumptions are indicated in parenthesis beside the calculated cross sections. E, denotes the level excitation energy. All cross sections are expressed in millibarns ,
IT---I/
E, / u measured ratios (MeV) , (meas .)
/
-I u (model calculations)
these are especially useful in making comparisons with model calculations. Here oi refers to the cross section to the i-th excited level. Model calculations are shown for several sets of spins and parities in columns 4-6 of table 1. The calculated ratio 02/uI is 0.44 assuming the 1st excited level is $-, and the ratio is 0.79 assuming $- for that level. This clearly rules out $- and leaves j- as an unambiguous assignment for the first excited level. With this and the ground state spin known, we have calculated cross sections for every feasible set of spin assignments for the Mn levels below 2.21 MeV. The only completely odd parity set of assignments which is consistent with all of the measurements is that shown in fig. 1, and for which calculated cross sections are listed in column 4 of table 1. Earlier but less complete work in this laboratory had indicated a preference for a i assignment to the 0.983 MeV level, and the calculations including that assumption are shown in column 5. They are not consistent with the measurements, and 4 is thus eliminated for that level. The only other possible set of spin assignments for which model and measurement are in reasonable agreement is shown in column 6. We reject this *****
212
LETTERS
15 April 1963
I.884 (3/2)-
1.527
H/2-
1.289
9/2-
-
7/25/2-
0.983
0.126
Mn55
Fig. 1. The low-lying levels of Mn55. The spin and parity assignments for the excited states are those based on this work.
set, however, for two reasons. First, the calculated ratios a3/a4, o4/02 yield 0.69 and 0.56, respectively. The same ratios obtained from the values in column 4 are 0.86 and 0.47. It is clear that the ratios from column 6 are not in agreement with the experimental ones, while those from column 4 are in agreement. Second, the positive parity assignment to a level at 1.289 MeV would require admixture of the 1% subshell, and such admixtures should not be important at low excitation for neutron and proton numbers well below 40. The spin and parity assignments shown in fig. 1 are therefore considered definite, except the i- assignment to the 1.527 MeV level. Assignments of either 6’ or 5’ to that level gave substantially the same set of calculated cross sections. The only basis for the I- choice is the expectation that a level at that excitation would have negative parity. It is interest, ing to note that, except for the position of the $level, the level order determined is that suggested by the weak surface coupling calculations of Ford and Levinson for an (f;)-3 configuration 8). This is the proton configuration of Mn55. 1) R. C. Lamb and M. T. McEllistrem, to be published. 2) E. M. Bernstein and H. W. Lewis, Phys. Rev. 100 (1955)
1367. 3) P. H. Stelson and F. K. McGowan, Reactions between complex nuclei (John Wiley and Sons, New York, 1960) p. 53. 4) N.Nath et al., Nuclear Phys. 13 (1959) 74. 5) J. W. Boring and M. T. McEllistrem, Phys. Rev. 124 (1961) 1531. Phys. Rev. 129 (1963) 727. 6) E.H.Schwarcz, 7) R. J. Howerton, Lawrence Radiation Laboratory Report UCRL-5573 (1961)) unpublished. 8) K.W. Ford and C. Levinson, Phys. Rev. 100 (1955) 1.
PHYSICS
LETTERS
The authors wish to thank Dr. C. A. Heras for a stimulating discussion.
3) 0. M. Bilaniuk and R. J. Slobodrian, to be published. 4) J.S. Blair, Phys. Rev. 115 (1959) 928, and references therein. 5) J.S. Blair, Proc. of the Int. Conf. on Nuclear Structure, Kingston, Canada (University of Toronto Press, Toronto, 1960) p. 827. 6) M.A.Preston, Physics of the nucleus (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962) Chapter 19. 7) Ray Satchler, private communication.
1) C.R. Lubitz, Numerical tables of Butler-Born approximation stripping cross sections (University of Michigan, Ann Arbor, Michigan, 1957), unpublished. 2) Vera Kistiakowsky-Fischer, Bull. Am. Phys. Sot. 2 (1957) 28.
SPIN
ASSIGNMENTS
IN Mn55
VIA
15 April 1963
INELASTIC
NEUTRON
SCATTERING
R. C. LAMB * and M. T. McELLISTREM University of Kentucky, Lexington, Kentucky ** Received 21 March 1963
The purpose of this letter is to present evidence for a definite spin sequence for the first three excited levels of Mn55 and for a tentative assignment for the fourth. These levels are located at 0.126, 0.983, 1.289 and 1.527 MeV. The basis for these assignments is a recently concluded series of measurements of inelastic neutron scattering 1). Recently published work, both experimental and theoretical, has indicated interest in but uncertainty about the spin assignments for the excited levels of Mn55. Previous spectroscopic work on the lowlying levels of Mn55 is summarised in the following four paragraphs. 1. A coulomb excitation study of the 0.126 MeV level had resulted in an assignment of i- for that level 2). However, a more recent study of this state has indicated that an assignment of s- or zis consistent with Coulomb excitation measurements 3). 2. Nath et al. have measured gamma ray production cross sections and level-decay branching ratios 4) for neutron energies between 1.2 MeV and 2.47 MeV. On the basis of their measurements, earlier scattering studies, and shell model expectations they suggested a spin sequence of $, 7 and $ for the second, third and fourth levels respectively. 3. Calculations presented in other work 5) on inelastic scattering in Mn55 have indicated a slight preference for a i assignment for the second excited state at 0.983 MeV rather than the tentative 5 assignment of Nath et al. 4. Finally, in a recent shell-model calculation 6) * National Science Foundation pre-doctoral
Fellow 1959-61. ** This work was partially supported by the United States Atomic Energy Commission.
of the level structure of Mn55 the spin and parity of the second excited state has been assumed to be i- in contrast to the 4 suggestion of Nath et al. The spin assignments presented in this letter are an effort to clarify the situation for the lowlying levels of Mn55. The use of inelastic neutron scattering as a spectroscopic tool depends on two principal assumptions. The first states that the neutron-nucleus interaction can be represented by a potential. The second is a conclusion of the statistical model, that the mode of decay of the compound system (n + target) is independent of its mode of formation. The potentials used to represent neutron inelastic scattering measurements have been those determined to fit the average dependence of total and elastic scattering cross sections as a function of energy and atomic weight. This representation has correctly discriminated between strong and weakly excited transitions, but good quantitative agreement between model calculations and measurements to individual final states has not been a general result. Hence the uncertainty in the interpretation of past inelastic scattering studies in Mn55. The study which is the basis for this letter includes a modified model for the calculation of the theoretical cross sections. The two assumptions mentioned above are retained, but the neutron-nucleus potential has been adjusted to force a fit to measured non-elastic cross sections and differential elastic cross sections 7) for the nucleus under study. With this model, the excitation of several states in each of the nuclei A127, Mn55 and Fe56 have been represented to well within the uncertainties on the measurements l). A result has been the spin and parity assignments reported here. Measured differential gamma ray production 211
Volume 4, number 4
PHYSICS
cross sections and decay branching ratios 1) yield the total inelastic scattering cross sections shown in table 1. The neutron bombarding energy was chosen as 2.21 MeV, since the Mn55 levels are easily resolved below that energy. The uncertainties shown are relative uncertainties, and an additional systematic uncertainty of vo is attributed to the magnitudes. Table 1 also contains several cross section ratios, with uncertainties, since Table 1 Measured and calculated neutron inelastic scattering cross sections in Mn55 for a neutron energy of 2.21 MeV. Also included are measured cross section ratios. The spin and parity assumptions are indicated in parenthesis beside the calculated cross sections. E, denotes the level excitation energy. All cross sections are expressed in millibarns ,
IT---I/
E, / u measured ratios (MeV) , (meas .)
/
-I u (model calculations)
these are especially useful in making comparisons with model calculations. Here oi refers to the cross section to the i-th excited level. Model calculations are shown for several sets of spins and parities in columns 4-6 of table 1. The calculated ratio 02/uI is 0.44 assuming the 1st excited level is $-, and the ratio is 0.79 assuming $- for that level. This clearly rules out $- and leaves j- as an unambiguous assignment for the first excited level. With this and the ground state spin known, we have calculated cross sections for every feasible set of spin assignments for the Mn levels below 2.21 MeV. The only completely odd parity set of assignments which is consistent with all of the measurements is that shown in fig. 1, and for which calculated cross sections are listed in column 4 of table 1. Earlier but less complete work in this laboratory had indicated a preference for a i assignment to the 0.983 MeV level, and the calculations including that assumption are shown in column 5. They are not consistent with the measurements, and 4 is thus eliminated for that level. The only other possible set of spin assignments for which model and measurement are in reasonable agreement is shown in column 6. We reject this *****
212
LETTERS
15 April 1963
I.884 (3/2)-
1.527
H/2-
1.289
9/2-
-
7/25/2-
0.983
0.126
Mn55
Fig. 1. The low-lying levels of Mn55. The spin and parity assignments for the excited states are those based on this work.
set, however, for two reasons. First, the calculated ratios a3/a4, o4/02 yield 0.69 and 0.56, respectively. The same ratios obtained from the values in column 4 are 0.86 and 0.47. It is clear that the ratios from column 6 are not in agreement with the experimental ones, while those from column 4 are in agreement. Second, the positive parity assignment to a level at 1.289 MeV would require admixture of the 1% subshell, and such admixtures should not be important at low excitation for neutron and proton numbers well below 40. The spin and parity assignments shown in fig. 1 are therefore considered definite, except the i- assignment to the 1.527 MeV level. Assignments of either 6’ or 5’ to that level gave substantially the same set of calculated cross sections. The only basis for the I- choice is the expectation that a level at that excitation would have negative parity. It is interest, ing to note that, except for the position of the $level, the level order determined is that suggested by the weak surface coupling calculations of Ford and Levinson for an (f;)-3 configuration 8). This is the proton configuration of Mn55. 1) R. C. Lamb and M. T. McEllistrem, to be published. 2) E. M. Bernstein and H. W. Lewis, Phys. Rev. 100 (1955)
1367. 3) P. H. Stelson and F. K. McGowan, Reactions between complex nuclei (John Wiley and Sons, New York, 1960) p. 53. 4) N.Nath et al., Nuclear Phys. 13 (1959) 74. 5) J. W. Boring and M. T. McEllistrem, Phys. Rev. 124 (1961) 1531. Phys. Rev. 129 (1963) 727. 6) E.H.Schwarcz, 7) R. J. Howerton, Lawrence Radiation Laboratory Report UCRL-5573 (1961)) unpublished. 8) K.W. Ford and C. Levinson, Phys. Rev. 100 (1955) 1.