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Mass and excited states of the nucleus ${}^{89}{Mo}$

R. C. Pardo, L. W. Robinson, W. Benenson, E. Kashy, and R. M. Ronningen

Phys. Rev. C 21, 462(R) (1980) - Published 1 January, 1980

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The mass excess of ${}^{89}{Mo}$ has been measured using the ${}^{92}{Mo}$ ( ${}^{3}{He}$ , ${}^{6}{He}$ ) reaction at 70-MeV bombarding energy. The mass excess was determined to be - 75.008 ± 0.015 MeV. The excited states observed are also reported.

NUCLEAR REACTIONS ${}^{92}{Mo}$ ( ${}^{3}{He}$ , ${}^{6}{He}$ ) ${}^{89}{Mo}$ ; $E = 70$ MeV, measured reaction $Q$ values, deduced mass excess, excitation energies.

RAPID COMMUNICATION

Band crossing in ${}^{172}{Hf}$

P. M. Walker, G. D. Dracoulis, and A. Johnston

Phys. Rev. C 21, 464(R) (1980) - Published 1 January, 1980

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The use of a multiplicity filter to enhance the observation of high-spin states following the ${}^{160}{Gd} ({}^{16}O, 4 n)$ reaction has enabled the yrast band to be seen up to spin $22^{+}$ . The energy of the $22^{+}$ → $20^{+}$ transition is consistent with that predicted recently in a band-crossing calculation.

NUCLEAR REACTIONS ${}^{160}{Gd} ({}^{16}O, 4 n)$ , $E = 87$ MeV; measured $γ - γ$ coin., $E γ$ , $γ - γ (θ)$ ; ${}^{172}{Hf}$ deduced levels; band-crossing model.

RAPID COMMUNICATION

Angular-momentum-dependent inertia parameter

Nazakat Ullah

Phys. Rev. C 21, 466(R) (1980) - Published 1 January, 1980

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Three-body Lippmann-Schwinger equations

Sadhan K. Adhikari and W. Glöckle

Phys. Rev. C 21, 54 (1980) - Published 1 January, 1980

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We present an alternative derivation of the necessary set of three-body Lippmann-Schwinger equations, which makes use of the asymptotic form of three-body scattering states in various channels and sheds light on certain possible traps. Thereby making explicit use of the identities for the channel resolvent operators, the homogeneous Lippmann-Schwinger equations are shown to be correct and consistent with the inhomogeneous one, contrary to a recent suggestion by Mukherjee.

NUCLEAR REACTIONS Three-body Lippmann-Schwinger equations, asymptotic behavior and nonuniqueness of solution.

Influence of vibrations of gas molecules on neutron reaction cross sections

C. D. Bowman and R. A. Schrack

Phys. Rev. C 21, 58 (1980) - Published 1 January, 1980

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The change in molecular vibrational energy upon absorption of a neutron by a nucleus bound in a free molecule can influence resonance shape and other aspects of neutron reaction cross sections. A formalism is developed for centrosymmetric molecules such as U $F_{6}$ and applied to the shape of the 6.67 eV resonance in ${}^{238}U$ . The ratio of the resonance shape for ${}^{238}U$ $F_{6}$ gas and for solid ${}^{238}U_{3}$ $O_{8}$ has been measured and compared with the calculation. Reasonable agreement is obtained indicating the validity of the calculation and the necessity to include vibration effects to avoid large errors in measurements and calculations on gascontaining systems.

NUCLEAR REACTIONS ${}^{238}U (n, γ)$ measured at 6.67 eV resonance; Effect of molecular vibrations studied experimentally and theoretically.

${}^{109}{Pd}$ : Difficulties in particle-rotor models for unique-parity states and revision of spectroscopic factors

R. F. Casten, G. J. Smith, M. R. Macphail, D. Breitig, W. R. Kane, M. L. Stelts, S. F. Mughabghab, J. A. Cizewski, H. G. Börner, W. F. Davidson, and K. Schreckenbach

Phys. Rev. C 21, 65 (1980) - Published 1 January, 1980

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Primary and secondary $γ$ rays following thermal and $p$ -wave resonant (2.96 eV) neutron capture on ${}^{108}{Pd}$ were measured to study $γ$ -ray transitions in ${}^{109}{Pd}$ . Average resonance capture spectra at 2 and 24 keV were also recorded and the ${}^{108}{Pd} (n, γ ce)$ reaction was studied and transition multipolarities were deduced. A detailed level scheme up to ∼1400 keV has been constructed. Numerous spin assignments have been revised, leading to substantial changes in the ( $d, p$ ) and ( $d, t$ ) spectroscopic factors, in particular for the $g_{\frac{7}{2}}$ orbit. The data on primary transition intensities for the 2.96 eV resonance are compared with the valence neutron capture model. The level scheme deduced for ${}^{109}{Pd}$ sheds new light on the previously proposed $g_{\frac{7}{2}} - h_{\frac{11}{2}}$ anomaly in the filling of these orbits, suggesting that, at least in ${}^{109}{Pd}$ , the appearance of the anomaly was largely due to spin misassignments. The revised systematics in the occupation of shell model orbits for a number of nuclei in this mass region is reviewed. Within the level scheme is a group of low-spin negative-parity levels which belong to the same family as the high-spin, decoupled, unique-parity states known in other odd mass Pd isotopes. These states correspond to the favored and unfavored anti-aligned levels for core rotations $R \leq 6$ . Calculations in the framework of the particle-rotor model cannot reproduce these level energies.

NUCLEAR REACTIONS ${}^{108}{Pd} (n, γ)$ , $E = thermal, 2.96 eV, 2 KeV, 24 KeV$ ; measured $E_{γ}$ , $I_{γ}$ , $I_{γ} (θ)$ ; ${}^{108}{Pd} (n, γ ce) {}^{108}{Pd}$ ${}^{109}{Pd}$ deduced $J$ , $π$ of 2.96 eV resonance, levels, transitions, multipolarities, $J$ , $π$ . Ge(Li) detectors, three crystal spectrometer, curved crystal spectrometers, conversion electron spectrometer, enriched targets.

NUCLEAR STRUCTURE ${}^{109}{Pd}$ revised ( $d, p$ ), ( $d, t$ ) spectroscopic factors, negative-parity anti-aligned favored and unfavored levels, particle-rotor model.

High-spin analog resonances near the $N = 50$ neutron shell

S. Galès, Y. El Hage, J. P. Schapira, S. Fortier, H. Laurent, and J. M. Maison

Phys. Rev. C 21, 98 (1980) - Published 1 January, 1980

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The ${}^{96}{Zr} ({}^{3}{He}, d) {}^{97}{Nb}$ and the ${}^{92}{Mo} ({}^{3}{He}, d) {}^{93}{Tc}$ reactions, investigated at, respectively, 39.0 and 28.5 MeV incident energies, were used to populate selectively high-spin analog resonances in ${}^{97}{Nb}$ and ${}^{93}{Tc}$ . Angular distributions were measured for the $d_{\frac{3}{2}}$ , $g_{\frac{7}{2}}$ , and $h_{\frac{11}{2}}$ analog states of the low-lying levels in ${}^{97}{Zr}$ . A distorted-wave Born-approximation analysis of the data for these unbound levels (using Gamow functions as form factors) was carried out and spectroscopic strengths extracted. The ${}^{96}{Zr} ({}^{3}{He}, d p)$ and ${}^{92}{Mo} ({}^{3}{He}, d p)$ reactions were performed, respectively, at 37.5 and 30 MeV incident energies. The angular distributions of the emitted protons were measured in coincidence using method II of Litherland and Ferguson with 0° detection of deuteron groups. Spins, population parameters, and proton branching ratios to the ground state and excited states of the targets were determined from the analysis of the angular correlation data. The position of the neutron threshold as compared with the excitation energies of the analog states in ${}^{97}{Nb}$ and ${}^{93}{Tc}$ is found to be an important parameter in the extraction of the structure information on core-excited components in the parent levels wave functions. Neutron particle-hole multiplets based on the ${(d_{\frac{5}{2}})}_{n}^{- 1} \otimes {(h_{\frac{11}{2}})}_{n}^{+ 1}$ and ${(d_{\frac{5}{2}})}_{n}^{- 1} \otimes {(g_{\frac{7}{2}})}_{n}^{+ 1}$ configurations are observed for the first time in ${}^{96}{Zr}$ through the decay of the $g_{\frac{7}{2}}$ and $h_{\frac{11}{2}}$ analog resonances. The limitation of the present method due to the neutron threshold or to the energy resolution in the proton channel is discussed and compared with the results of inelastic resonant scattering through isobaric analog resonances.

NUCLEAR REACTIONS ${}^{92}{Mo} ({}^{3}{He}, d)$ $E = 28.5$ MeV; measured $σ (E_{d}, θ)$ , $θ = 20 °, 35 °$ . ${}^{96}{Zr} ({}^{3}{He}, d)$ $E = 39.0$ MeV; measured $σ (E_{d}, θ)$ . ${}^{92}{Mo} ({}^{3}{He}, d \tilde{p})$ $E = 30$ MeV, ${}^{96}{Zr} ({}^{3}{He}, d \tilde{p})$ $E = 37.5$ MeV; measured $σ (E_{d}, E_{p}, θ_{P})$ . ${}^{93}{Tc}$ , ${}^{97}{Nb}$ deduced IAS, $L$ , $J$ , $π$ , $S$ , $Γ_{p}$ , $Γ_{p^{'}}$ . DWBA analysis using Gamow functions as form factors. Magnetic analysis. Enriched targets.

Redundant solutions, scattering solutions, and nonsymmetric nonlocal potentials

B. Bagchi and B. Mulligan

Phys. Rev. C 20, 1973 (1979) - Published 1 December, 1979

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Increasingly, nonsymmetric nonlocal potentials are occurring in formulations which include descriptions of antisymmetrization and other nuclear phenomena. In studying such potentials, it is found that the characteristics of solutions of the scattering equation differ in some cases significantly from those associated with symmetric nonlocal potentials. For example, it has been demonstrated that when redundant solutions are present due to antisymmetrization, a scattering solution does not exist unless a consistency condition is satisfied. In the present paper this and other such aspects of nonsymmetric nonlocal potentials are investigated. The importance of the adjoint potential to these discussions is particularly emphasized. Conditions on scattering solutions for nonsymmetric nonlocal potentials and their adjoints are discussed in detail, and an example is presented.

NUCLEAR REACTIONS Antisymmetrization, scattering solutions for a nonlocal potential, nonsymmetric nonlocal potentials, scattering solutions for adjoint potentials, Fredholm determinants, redundant states.

Cross sections for the ${}^{6}{Li}$ ( $p$ , ${}^{3}{He}$ ) ${}^{4}{He}$ reaction at energies between 0.1 and 3.0 MeV

A. J. Elwyn, R. E. Holland, C. N. Davids, L. Meyer-Schützmeister, F. P. Mooring, and W. Ray, Jr.

Phys. Rev. C 20, 1984 (1979) - Published 1 December, 1979

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Absolute differential and total (integrated) cross sections for the ${}^{6}{Li}$ ( $p$ , ${}^{3}{He}$ ) ${}^{4}{He}$ reaction at proton energies between ∼0.14 and 3 MeV are presented, and compared with previous measurements. The results comprise a consistent set of data over much of the energy range of interest to a number of applications. Thermonuclear reaction rate parameters and astrophysical $S$ factors are calculated. The measured angular distributions are compared to predictions of a preliminary $R$ -matrix analysis based on the nuclear properties of energy levels in the mass-7 system.

NUCLEAR REACTIONS ${}^{6}{Li}$ ( $p$ , ${}^{3}{He}$ ) ${}^{4}{He}$ , $E_{p} = 0.14 - 3$ MeV; enriched target; measured $σ (E_{p}, θ)$ , $σ (E_{p})$ ; calculated $〈 σ v 〉$ , astrophysical $S$ factor.

Inelastic proton scattering and particle-vibration coupling in ${}^{115}{Sn}$ , ${}^{117}{Sn}$ , and ${}^{119}{Sn}$

Donald G. Fleming, F. D. Becchetti, and Edward R. Flynn

Phys. Rev. C 20, 1993 (1979) - Published 1 December, 1979

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Inelastic proton scattering on the stable odd- $A$ tin isotopes ${}^{115}{Sn}$ , ${}^{117}{Sn}$ , and ${}^{119}{Sn}$ has been carried out at 18 MeV on isotope separated targets. Angular distributions were not obtained but, nevertheless, the individual spectra reveal a large number of strongly populated states in the energy region of the known octupole strength of the even- $A$ nuclei, permitting several new (tentative) $\frac{5}{2^{-}}$ , $\frac{7}{2^{-}}$ spin assignments. General comparisons are made of the observed relative strengths with those obtained from other reactions populating the same final states, revealing a complex nuclear structure in the odd- $A$ tins which is not understood theoretically.

NUCLEAR REACTIONS, NUCLEAR STRUCTURE ${}^{115}{Sn}$ , ${}^{117}{Sn}$ , ${}^{119}{Sn}$ ( $p$ , $p^{'}$ ); isotope separated targets; 18 MeV, 15 keV resolution; relative intensities only; new ${\frac{5}{2}}^{-}$ , ${\frac{7}{2}}^{-}$ spin assignments.

Resonating-group study of the $α$ + ${}^{15}N$ system

M. LeMere and Y. C. Tang

Phys. Rev. C 20, 2003 (1979) - Published 1 December, 1979

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The resonating-group method is used to study the $α$ + ${}^{15}N$ system. The result shows that, with the use of a reasonable nucleon-nucleon interaction and a phenomenological imaginary potential, the calculation can yield a differential cross section which agrees rather well with experimental data. In addition, one learns from this study useful information concerning the cluster structures of many bound and resonance levels in the compound nucleus ${}^{19}F$ .

NUCLEAR REACTIONS ${}^{15}N$ ( $α$ , $α$ ); calculated level structure, phase shifts, and $σ (θ)$ . Resonating-group method.

Hole states excited by the ${}^{24}{Mg}$ ( $p$ , $d$ ) ${}^{23}{Mg}$ reaction at 95 MeV

D. W. Miller, W. P. Jones, D. W. Devins, R. E. Marrs, and J. Kehayias

Phys. Rev. C 20, 2008 (1979) - Published 1 December, 1979

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Experimental excitation energies and angular distributions have been obtained for 33 deuteron groups from the ${}^{24}{Mg}$ ( $p$ , $d$ ) reaction at 94.8-MeV bombarding energy with 80-keV experimental resolution. Energies obtained for states in ${}^{23}{Mg}$ are in agreement with the sixth compilation of Endt and van der Leun up to 7.25 MeV and the recent unpublished ( $p$ , $t$ ) study of Nann et al. up to 9.72 MeV. Energies are determined in the present work for 18 additional groups corresponding to excitations between 9.8 and 13.28 MeV. Angular distributions from 6° to 88° laboratory (momentum transfers up to 660 MeV/c) show characteristic oscillatory signatures for $l = 0$ transitions and broad peaked nonoscillatory behavior for presumed multistep transitions. $l = 1 and 2$ transitions show a very similar exponential falloff with large momentum transfer, but they can be clearly distinguished by their small-angle behavior after division by an empirical exponential factor or by the dominant momentum transfer dependence from a plane-wave analysis. $l = 1$ transitions are observed to deep-hole states at 8.91-, 9.02-, 9.67-, and 10.57-MeV excitation. The angular distributions also lead to very probable assignments of $\frac{5}{2^{-}}$ and $\frac{7}{2^{+}}$ to the 3.97- and 4.68-MeV states of ${}^{23}{Mg}$ , and are consistent with $\frac{9}{2^{+}}$ and $\frac{11}{2^{+}}$ assignments to the 2.71- and 5.45-MeV states. Distorted-wave Born approximation (DWBA) predictions using optical potentials from published elastic scattering results show rather good agreement with the shapes of the observed angular distributions for $l = 2$ transitions, but spectroscopic factors vary by up to a factor of 3 depending on the deuteron potential employed. $l = 0$ transitions are not fitted in either shape or position of the oscillations, which may be due to the fact that deuteron wave functions derived from elastic scattering are not accurate in the nuclear interior. Reasonable shapes are predicted by preliminary coupled-channel Born approximation (CCBA) analyses for transitions believed to proceed in two steps.

NUCLEAR REACTIONS ${}^{24}{Mg}$ ( $p$ , $d$ ), $E = 94.8$ MeV; measured $σ (θ)$ . ${}^{23}{Mg}$ levels deduced $l$ , $J$ , $π$ . $S$ . DWBA analysis, resolution 80 keV, $θ = 6 ° - 88 °$ , $Δ θ = 2 ° or 4 °$ , $E_{x} = 0 - 13.28$ MeV.

Experiment and theory for the reaction ${}^{7}{Li}$ ( $γ$ , $t$ ) ${}^{4}{He}$ for $E_{γ} < 50$ MeV

D. M. Skopik, J. Asai, E. L. Tomusiak, and J. J. Murphy, II

Phys. Rev. C 20, 2025 (1979) - Published 1 December, 1979

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Differential and total cross sections for the ${}^{7}{Li}$ ( $γ$ , $t$ ) ${}^{4}{He}$ reaction were measured. Both real and virtual photons were used in the experiment and gave self-consistent results. The data show a broad resonance indicating the presence of positive parity states near 8 MeV excitation in ${}^{7}{Li}$ . A calculation using an $α$ - ${}^{3}H$ cluster model of ${}^{7}{Li}$ was also performed. Poor agreement is found between the calculation and experimental results.

NUCLEAR REACTIONS ${}^{7}{Li}$ ( $γ$ , $t$ ) ${}^{4}{He}$ , measured $σ (E; E_{α}, θ_{α})$ and (( $E$ ; $E_{t}$ , $θ_{t}$ )) calculated ${}^{3}H$ - $α$ cluster model cross section.

Two-particle two-hole configurations in ${}^{208}{Bi}$ and the ${}^{210}{Bi}^{m} (p, t) {}^{208}{Bi}$ reaction

K. A. Erb, W. D. Callender, and R. K. Sheline

Phys. Rev. C 20, 2031 (1979) - Published 1 December, 1979

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Levels in ${}^{208}{Bi}$ were studied using the ${}^{210}{Bi}^{m} (p, t) {}^{208}{Bi}$ reaction at 18.4 MeV. The target isomeric state employed in the reaction was the $9^{-}$ , 271 keV, 3 × $10^{6}$ year second-excited state of ${}^{210}{Bi}$ . The measured angular distributions for the positive parity ( $π h_{\frac{9}{2}}$ , $ν^{- 1}$ ) particle-hole multiplets were well described by distorted-waves calculations using the shell model wave functions of Kuo. However, the data for the negative parity ( $π h_{\frac{9}{2}}$ , $ν^{- 1} i_{\frac{13}{2}}$ ) levels were poorly reproduced by these calculations, and evidence was found for the presence of two-particle two-hole admixtures in the $9^{-}$ , $10^{-}$ , and $11^{-}$ members of this multiplet. In addition, a number of previously unobserved levels were identified in ${}^{208}{Bi}$ , and several of these were populated in the reaction with considerably enhanced cross sections. The excitation energies and differential cross sections for the latter group of levels were found to be characteristic of two-particle two-hole states in ${}^{208}{Bi}$ consisting of $π h_{\frac{9}{2}}$ , $ν g_{\frac{9}{2}}$ particles coupled to the $0_{1}^{+}$ and $2_{1}^{+}$ excitations of ${}^{206}{Pb}$ .

NUCLEAR REACTIONS ${}^{210}{Bi}^{m} (p, t) {}^{208}{Bi}$ , $E = 18.4$ MeV; measured $σ (θ)$ . ${}^{208}{Bi}$ deduced levels, $J$ , $π$ . Radioactive, enriched target. DWBA analysis, tested shell model wave functions.

Energy levels below 2 MeV in ${}^{121}{Sb}$ and ${}^{123}{Sb}$

H. R. Hooper, P. W. Green, H. E. Siefken, G. C. Neilson, W. J. McDonald, D. M. Sheppard, and W. K. Dawson

Phys. Rev. C 20, 2041 (1979) - Published 1 December, 1979

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Energy levels below 2 MeV in ${}^{121}{Sb}$ and ${}^{123}{Sb}$ have been studied using the ${}^{121, 123}{Sb}$ ( $n$ , $n^{'} γ$ ) and ${}^{120}{Sn}$ ( $p$ , $γ$ ) reactions. $γ$ -ray angular distributions have been measured and spins and $γ$ -ray multipole mixing ratios deduced. Spin assignments have been made for the $1025 (\frac{7}{2})$ , $1036 (\frac{9}{2})$ , and $1145 (\frac{9}{2})$ keV levels in ${}^{121}{Sb}$ , and an assignment of $\frac{9}{2}$ is suggested for the 1030 keV level in ${}^{123}{Sb}$ . Present and previous results are discussed in the framework of an intermediate coupling model.

NUCLEAR REACTIONS ${}^{121, 123}{Sb}$ ( $n$ , $n^{'} γ$ ), $E = 1.5 - 2.7$ MeV; measured $E_{γ}$ , $σ (E_{γ}, θ_{γ})$ , branching ratios; ${}^{121, 123}{Sb}$ deduced levels, $J$ , $δ$ ; natural targets. ${}^{120}{Sn}$ ( $p$ , $γ$ ), $E = 3.4$ MeV; measured $E_{γ}$ ; enriched target. Intermediate coupling model calculations.

( $p$ , $n$ ) reaction for $89 < A < 130$ and an anomalous optical model potential for sub-Coulomb protons

C. H. Johnson, A. Galonsky, and R. L. Kernell

Phys. Rev. C 20, 2052 (1979) - Published 1 December, 1979

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The ( $p$ , $n$ ) cross sections were measured from about 2.5 to 5.8 MeV with about 100-keV target resolution for natural Pd, Ag, Cd, In, and Te and for ${}^{89}Y$ , ${}^{93}{Nb}$ , ${}^{103}{Rh}$ , ${}^{105, 106, 108, 110}{Pd}$ , ${}^{107, 109}{Ag}$ , ${}^{111, 112, 113, 114, 116}{Cd}$ , and ${}^{125, 126, 128, 130}{Te}$ . Systematic uncertainties are about ±2% for ${}^{89}Y$ , ${}^{93}{Nb}$ , and the natural targets and about ±4% for the other nuclei. The isotopic $σ_{p, n}$ are fitted by adjustment in the depth $W_{D}$ and diffuseness $a_{D}$ of the surface imaginary part of a proton optical model potential (OMP) that was chosen previously to describe precision ( $p$ , $n$ ) data for isotopes of Sn. The diffuseness $a_{D}$ is found to be nearly constant, about 0.4 fm, but the depth $W_{D}$ shows a large and systematic $A$ dependence. A study of the parameter space indicates that at least one OMP parameter must have a strong $A$ dependence and that $W_{D}$ is probably the only such single parameter that will suffice. The explanation of this anomaly is currently unclear.

NUCLEAR REACTIONS: Pd, Ag, Cd, In, Te, natural targets; and ${}^{89}Y$ , ${}^{93}{Nb}$ , ${}^{103}{Rh}$ , ${}^{105, 106, 108, 110}{Pd}$ , ${}^{107, 109}{Ag}$ , ${}^{111, 112, 113, 114, 116}{Cd}$ , ${}^{125, 126, 128, 130}{Te}$ , enriched isotopic targets, $E = 2.5 to 5.8$ MeV, target resolution ∼ 100 keV. Measured $σ_{p, n}$ . Deduced optical model parameters.

Gamma-ray strength functions for ${}^{104}{Rh}$ , ${}^{170}{Tm}$ , and ${}^{198}{Au}$

S. Joly, D. M. Drake, and L. Nilsson

Phys. Rev. C 20, 2072 (1979) - Published 1 December, 1979

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Gamma-ray spectra following neutron capture in rhodium, thulium, and gold for neutron energies between 0.5 and 3.0 MeV have been measured with a NaI scintillator surrounded by an annular NaI crystal. The $γ$ -ray strength functions were deduced from the capture $γ$ -ray spectra by the spectrum fitting method. A bump around 6 MeV is observed for gold as well as a smaller one around 3.5 MeV for thulium. The present results are compared with extrapolations of giant dipole resonance data and measured average total radiative widths.

NUCLEAR REACTIONS ${}^{103}{Rh}$ , ${}^{169}{Tm}$ , ${}^{197}{Au}$ (( $n$ , $γ$ ),), $E_{n} = 0.5 - 3.0$ MeV, measured $σ (E_{n}, E_{γ})$ . Deduced $γ$ -ray strength functions. Comparison with other data.

Multipole moments of ${}^{154}{Sm}$ , ${}^{176}{Yb}$ , ${}^{232}{Th}$ , and ${}^{238}U$ from proton inelastic scattering

C. H. King, J. E. Finck, G. M. Crawley, J. A. Nolen, Jr., and R. M. Ronningen

Phys. Rev. C 20, 2084 (1979) - Published 1 December, 1979

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We have measured the inelastic scattering of 35 MeV protons from the nuclei ${}^{154}{Sm}$ , ${}^{176}{Yb}$ , ${}^{232}{Th}$ , and ${}^{238}U$ . Angular distributions were extracted for $J^{π} = 0^{+} - 8^{+}$ members of ground state rotational bands. These data were analyzed using coupled channels calculations for scattering from a deformed optical potential. Searches were made on some of the parameters of this potential, including the deformation parameters $β_{2}$ and $β_{4}$ . The multipole moments of the potential distribution were calculated from the parameter values and are compared to the results of Coulomb excitation, electron scattering, and inelastic, alpha-particle scattering studies. In general, these moments deduced in our investigation agree better with those from Coulomb excitation and electron scattering than with moments deduced from $α$ -particle scattering. But we also find the moments from our study to be systematically smaller than those from Coulomb excitation.

NUCLEAR REACTIONS ${}^{154}{Sm}$ ( $p$ , $p^{'}$ ), ${}^{176}{Yb}$ ( $p$ , $p^{'}$ ), ${}^{232}{Th}$ ( $p$ , $p^{'}$ ), and ${}^{238}U$ ( $p$ , $p^{'}$ ), $E_{p} = 35$ MeV; enriched targets, nuclear emulsion plates (7 keV FWHM) and position-sensitive proportional counter (15 keV FWHM), magnetic spectrograph; measured $σ (E p^{'}, θ)$ ; coupled channels calculations, rotational model; deduced optical model and deformation parameters, quadrupole and hexadecapole moments; comparisons to Coulomb excitation, ( $e$ , $e^{'}$ ) and ( $α$ , $α^{'}$ ), comparisons to Hartree-Fock calculations.

Coulomb excitation of ${}^{183}W$

F. K. McGowan, C. E. Bemis, Jr., J. L. C. Ford, Jr., W. T. Milner, D. Shapira, and P. H. Stelson

Phys. Rev. C 20, 2093 (1979) - Published 1 December, 1979

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Direct $E 2$ and multiple Coulomb excitation of states up to $J = \frac{9}{2}$ in the $K = \frac{1}{2}$ and $K = \frac{3}{2}$ bands of ${}^{183}W$ has been measured by means of $γ$ -ray spectroscopy. Excitation was produced by 15-MeV ${}^{4}{He}$ ions on a thick target of W with natural abundance. Excitation probabilities were also determined relative to the elastic scattering by the observation of the ( $α$ , $α^{'}$ ) reaction on ${}^{183}W$ with 13-MeV ${}^{4}{He}$ ions using a split-pole magnetic spectrometer equipped with a position-sensitive proportional detector. The $B (E 2)$ values for excitation of the $\frac{3}{2^{L}}$ , $\frac{5}{2^{L}}$ , $\frac{3}{2^{H}}$ , and $\frac{5}{2^{H}}$ states ( $H$ and $L$ refer to the high and low energy states of the same total angular momentum $J$ ) are obtained and information is given on the reduced transition probabilities for the different decay modes of these states. In particular, the prediction of strong cancellation in the $E 2$ transition probabilities for the $\frac{3}{2^{H}} \to \frac{1}{2^{L}}$ , $\frac{3}{2^{H}} \to \frac{5}{2^{L}}$ , and $\frac{5}{2^{H}} \to \frac{5}{2^{L}}$ transitions from Coriolis interaction calculations has been verified by the experimental results. The experimental results are compared with several calculations of the Coriolis coupling between the rotational bands. Several weakly excited states between 0.9 and 1.5 MeV were observed and the $B (E 2)$ for excitation of these states are $\leq B {(E 2)}_{s . p .}$ .

NUCLEAR REACTIONS ${}^{183}W$ ( $α$ , $α^{'} γ$ ), $E = 15$ MeV, ${}^{183}W$ ( $α$ , $α^{'}$ ), $E = 13$ MeV; measured $E_{γ}$ , $I_{γ}$ , $γ (θ)$ , $σ (E_{α^{'}}; θ = 150)$ ; ${}^{183}W$ levels deduced $B (E 2)$ , $B (M 1)$ , $J^{π}$ , $δ$ . Enriched target.

Level structure of ${}^{92}{Zr}$ from the ( $d$ , $p$ ) reaction on ${}^{91}{Zr}$

T. Borello-Lewin, H. M. A. Castro, L. B. Horodynski-Matsushigue, and O. Dietzsch

Phys. Rev. C 20, 2101 (1979) - Published 1 December, 1979

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Levels in ${}^{92}{Zr}$ were studied by a high resolution ( $d$ , $p$ ) reaction on ${}^{91}{Zr}$ . Outgoing particles were momentum analyzed in a split-pole spectrograph and detected in nuclear emulsion plates. A total of 64 levels was identified up to about 5.4 MeV of excitation, several of them not previously reported. Experimental angular distributions were compared to distorted-wave Born-approximation predictions and reduced spectroscopic factors obtained. Energies of centers of gravity of each shell-model orbital were deduced and effective ${(d_{\frac{5}{2}})}^{2}$ and ( $s_{\frac{1}{2}} d_{\frac{5}{2}}$ ) neutron-neutron two-body diagonal matrix elements were estimated.

NUCLEAR REACTIONS ${}^{91}{Zr}$ ( $d$ , $p$ ), $E = 12$ MeV; measured $σ (E_{p}, θ)$ . ${}^{92}{Zr}$ deduced levels $l$ , $J$ , $π$ , reduced spectroscopic factors. Enriched targets.

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Physical Review C

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Mass and excited states of the nucleus ${}^{89}{Mo}$

Band crossing in ${}^{172}{Hf}$

Angular-momentum-dependent inertia parameter

Three-body Lippmann-Schwinger equations

Influence of vibrations of gas molecules on neutron reaction cross sections

${}^{109}{Pd}$ : Difficulties in particle-rotor models for unique-parity states and revision of spectroscopic factors

High-spin analog resonances near the $N = 50$ neutron shell

Redundant solutions, scattering solutions, and nonsymmetric nonlocal potentials

Cross sections for the ${}^{6}{Li}$ ( $p$ , ${}^{3}{He}$ ) ${}^{4}{He}$ reaction at energies between 0.1 and 3.0 MeV

Inelastic proton scattering and particle-vibration coupling in ${}^{115}{Sn}$ , ${}^{117}{Sn}$ , and ${}^{119}{Sn}$

Resonating-group study of the $α$ + ${}^{15}N$ system

Hole states excited by the ${}^{24}{Mg}$ ( $p$ , $d$ ) ${}^{23}{Mg}$ reaction at 95 MeV

Experiment and theory for the reaction ${}^{7}{Li}$ ( $γ$ , $t$ ) ${}^{4}{He}$ for $E_{γ} < 50$ MeV

Two-particle two-hole configurations in ${}^{208}{Bi}$ and the ${}^{210}{Bi}^{m} (p, t) {}^{208}{Bi}$ reaction

Energy levels below 2 MeV in ${}^{121}{Sb}$ and ${}^{123}{Sb}$

( $p$ , $n$ ) reaction for $89 < A < 130$ and an anomalous optical model potential for sub-Coulomb protons

Gamma-ray strength functions for ${}^{104}{Rh}$ , ${}^{170}{Tm}$ , and ${}^{198}{Au}$

Multipole moments of ${}^{154}{Sm}$ , ${}^{176}{Yb}$ , ${}^{232}{Th}$ , and ${}^{238}U$ from proton inelastic scattering

Coulomb excitation of ${}^{183}W$

Level structure of ${}^{92}{Zr}$ from the ( $d$ , $p$ ) reaction on ${}^{91}{Zr}$

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