Deconvolution of the Photon Strength Function
183
in the photonuclear and Oslo LDFs at all energies. Oslo experiments also populate
a much larger range of level spins and parities that may deexcite by M1, E2, and
nuclear structure related E1 transitions.
The Oslo GSF, f Oslo ↓ (E γ ) can be deconvoluted from the Oslo PSF by dividing
out their experimental level densities, ρ Oslo (E x , J π ) as shown in Eq. 6
f Oslo ↓ (E γ ) ∝
F Oslo ↓ (E γ )
ρ Oslo (E x , J π )
.
(6)
No exact normalization is possible for these data; however, the relative GSF trends
can be inferred. Also, no B(σ L) matrix elements can be inferred because f Oslo ↓
(E γ ) represents a composite strength for all multipolarities. Indeed there is no
evidence that a constant, energy dependent, GSF is even appropriate for M1, E2,
and some E1 transitions.
Renormalized Oslo reaction GSFs for 92−98 Mo [9, 10] are compared with the
corresponding photonuclear GSFs in Fig. 2. The photonuclear GSFs are calculated
with the BA formulation using RIPL-3 [11] GDR parameters. Here the Oslo GSF
data are normalized so that no values fall below the BA values. In all cases the
Oslo GSFs show significant enhancement at both low and high γ -ray energies. The
low-energy enhancement is consistent with earlier shell model calculations [12] for
56,57 Fe and can be ascribed to M1 transitions between levels of the same seniority.
The high-energy enhancement is consistent with bremsstrahlung measurements on
the same isotopes and has been ascribed [13] to pygmy resonances.
I have demonstrated that PSFs can be deconvoluted into the product of a LDF and
a GSF. The photonuclear GSF is a nearly continuous function that decreases rapidly
with increasing transition energy, as would be expected if the nuclear structures of
widely separated levels are very different. A new method is described for extracting
the Oslo GSF from their PSF data. The Oslo GSF for the isotopes 92−98 Mo has been
analyzed and reveals both low- and high-energy upbends in all cases.
Acknowledgments This work was performed under the auspices of the U.S. Department of
Energy by the University of California, supported by the Director, Office of Science, Office
of Basic Energy Sciences, of the U.S. Department of Energy at Lawrence Berkeley National
Laboratory under Contract No. DE-AC02-05CH11231. I especially wish to thank my colleagues
at the University of Oslo for our many scientific discussions and their hospitality during my many
visits there that inspired my interest in this subject.
References
1. A. Schiller, L. Bergholt, M. Guttormsen, E. Melby, J. Rekstad, S. Siem, Extraction of level
density and γ strength function from primary γ spectra. Nucl. Instrum. Methods 447, 498
(2000)
2. J. Blatt, V. Weisskop, Theoretical Nuclear Physics (John Wiley and Sons, New York, 1952)
183
in the photonuclear and Oslo LDFs at all energies. Oslo experiments also populate
a much larger range of level spins and parities that may deexcite by M1, E2, and
nuclear structure related E1 transitions.
The Oslo GSF, f Oslo ↓ (E γ ) can be deconvoluted from the Oslo PSF by dividing
out their experimental level densities, ρ Oslo (E x , J π ) as shown in Eq. 6
f Oslo ↓ (E γ ) ∝
F Oslo ↓ (E γ )
ρ Oslo (E x , J π )
.
(6)
No exact normalization is possible for these data; however, the relative GSF trends
can be inferred. Also, no B(σ L) matrix elements can be inferred because f Oslo ↓
(E γ ) represents a composite strength for all multipolarities. Indeed there is no
evidence that a constant, energy dependent, GSF is even appropriate for M1, E2,
and some E1 transitions.
Renormalized Oslo reaction GSFs for 92−98 Mo [9, 10] are compared with the
corresponding photonuclear GSFs in Fig. 2. The photonuclear GSFs are calculated
with the BA formulation using RIPL-3 [11] GDR parameters. Here the Oslo GSF
data are normalized so that no values fall below the BA values. In all cases the
Oslo GSFs show significant enhancement at both low and high γ -ray energies. The
low-energy enhancement is consistent with earlier shell model calculations [12] for
56,57 Fe and can be ascribed to M1 transitions between levels of the same seniority.
The high-energy enhancement is consistent with bremsstrahlung measurements on
the same isotopes and has been ascribed [13] to pygmy resonances.
I have demonstrated that PSFs can be deconvoluted into the product of a LDF and
a GSF. The photonuclear GSF is a nearly continuous function that decreases rapidly
with increasing transition energy, as would be expected if the nuclear structures of
widely separated levels are very different. A new method is described for extracting
the Oslo GSF from their PSF data. The Oslo GSF for the isotopes 92−98 Mo has been
analyzed and reveals both low- and high-energy upbends in all cases.
Acknowledgments This work was performed under the auspices of the U.S. Department of
Energy by the University of California, supported by the Director, Office of Science, Office
of Basic Energy Sciences, of the U.S. Department of Energy at Lawrence Berkeley National
Laboratory under Contract No. DE-AC02-05CH11231. I especially wish to thank my colleagues
at the University of Oslo for our many scientific discussions and their hospitality during my many
visits there that inspired my interest in this subject.
References
1. A. Schiller, L. Bergholt, M. Guttormsen, E. Melby, J. Rekstad, S. Siem, Extraction of level
density and γ strength function from primary γ spectra. Nucl. Instrum. Methods 447, 498
(2000)
2. J. Blatt, V. Weisskop, Theoretical Nuclear Physics (John Wiley and Sons, New York, 1952)