Recent Articles

Erratum: 28- and 34-MeV ${}^{6}{Li}$ and ${}^{7}{Li}$ elastic scattering on nuclei with $40 \leq A \leq 91$

R. I. Cutler, M. J. Nadworny, and K. W. Kemper

Phys. Rev. C 16, 1692 (1977) - Published 1 October, 1977

Gamma rays from thermal neutron capture in ${}^{136}{Xe}$

Stanley G. Prussin, Robert G. Lanier, Gordon L. Struble, Lloyd G. Mann, and Susan M. Schoenung

Phys. Rev. C 16, 1001 (1977) - Published 1 September, 1977

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The $γ$ - ray spectrum following thermal neutron capture in ${}^{136}{Xe}$ has been studied with a Compton-suppression spectrometer. The $Q$ value for the reaction has been measured as $Q (n, γ) = 4025.5 \pm 0.3$ keV. Levels populated by primary transitions from the capture state correlate well with those populated by $l = 1$ transfers in the ( $d, p$ ) and ( $p, p_{0}$ ) reactions. The data indicate a strong correlation between reduced transition probabilities for the primary transitions and spectroscopic factors for final levels.

NUCLEAR REACTIONS ${}^{136}{Xe} (n_{th}, γ) {}^{137}{Xe}$ ; measured $E_{γ}$ , $I_{γ}$ ; Ge(Li) Compton suppression spectrometer; deduced $Q$ ; ${}^{137}{Xe}$ deduced levels, $J$ , $π$ .

Isotope and element distributions of the evaporation residues from fusion of 160 MeV ${}^{32}S$ with ${}^{24, 25, 26}{Mg}$ and ${}^{27}{Al}$

F. Pühlhofer, W. F. W. Schneider, F. Busch, J. Barrette, P. Braun-Munzinger, C. K. Gelbke, and H. E. Wegner

Phys. Rev. C 16, 1010 (1977) - Published 1 September, 1977

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Evaporation residues from fusion reactions induced by 160 MeV ${}^{32}S$ on targets of ${}^{24, 25, 26}{Mg}$ and ${}^{27}{Al}$ were identified by means of a time-of-flight $Δ E - E$ detector telescope. Angular distributions were measured in the range from 3° to 16° and total yields were determined as a function of $A$ and $Z$ of the products. The mass distributions of the evaporation residues (summed over $Z$ ) show the typical structure arising from the competition between nucleon and $α$ -evaporation in the decay of the highly excited (83 to 90 MeV) compound nuclei, with only little variation between the four systems. It is concluded that the deexcitation mechanism is to a large extent independent of the individual structure of the nuclei in the decay chains. This is also demonstrated by the yield distributions for the individual nuclides, in particular by the similarity of the yield patterns obtained in the $N - Z$ plane for the compund nuclie ${}^{59}{Cu}$ and ${}^{57}{Ni}$ . The data are reproduced very well by evaporation calculations based on the statistical theory. Effects of nuclear deformations due to the high angular monentum on the shape of the yrast line and on the transmission coefficients for the emitted light particles were included. The influence of shell effects in the level densities at high excitation was studied and found to be negligible above 15 MeV excitation.

NUCLEAR REACTIONS ${}^{32}S$ on ${}^{24}{Mg}$ , ${}^{25}{Mg}$ , ${}^{26}{Mg}$ , ${}^{27}{Al}$ , $E = 160.7$ MeV $σ (θ, A, Z)$ for fusion products. Discussed systematics of nuclide distributions as function of compound-nucleus mass. Comparison with evaporation calculations, shell effects in level densities studied.

Nuclear shapes of ${}^{24}{Mg}$ and ${}^{28}{Si}$ by inelastic scattering of ${}^{12}C$ and ${}^{16, 18}O$

John S. Eck, D. O. Elliott, W. J. Thompson, and F. Todd Baker

Phys. Rev. C 16, 1020 (1977) - Published 1 September, 1977

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The measurement and analysis of the differential cross sections for the elastic and inelastic scattering to the lowest $2^{+}$ states of ${}^{24}{Mg}$ and ${}^{28}{Si}$ in the scattering of ${}^{12}C$ at bombarding energies of 25 and 30 MeV are reported. In addition, elastic and inelastic scattering for ${}^{16}O$ + ${}^{24}{Mg}$ , ${}^{16}O$ + ${}^{28}{Si}$ , and ${}^{18}O$ + ${}^{28}{Si}$ , which had been measured previously, are reanalyzed. The analyses are carried out utilizing a coupled-channels code, and deformation lengths for ${}^{24}{Mg}$ and ${}^{28}{Si}$ are determined from the scattering of the different projectiles. The deformation lengths extracted from these analyses are compared with each other and with the results of a recently reported systematic investigation of deformation lengths in light nuclei.

NUCLEAR REACTIONS ${}^{24}{Mg}$ ( ${}^{12}C$ , ${}^{12}C$ ), ${}^{24}{Mg}$ ( ${}^{12}C$ , ${}^{12}C$ ) ${}^{24}{Mg}^{*}$ $Q = - 1.37$ MeV, $E = 25 and 30$ MeV; ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{16}O$ ), ${}^{24}{Mg}$ ( ${}^{16}O$ , ${}^{16}O$ ) ${}^{24}{Mg}^{*}$ $Q = - 1.37$ MeV, $E = 36$ MeV; ${}^{28}{Si}$ ( ${}^{12}C$ , ${}^{12}C$ ), ${}^{28}{Si}$ ( ${}^{12}C$ , ${}^{12}C$ ) ${}^{28}{Si}^{*}$ $Q = - 1.78$ MeV, $E = 25 and 30$ MeV; ${}^{28}{Si}$ ( ${}^{16}O$ , ${}^{16}O$ ), ${}^{28}{Si}$ ( ${}^{16}O$ ) ${}^{28}{Si}^{*}$ $Q = - 1.78$ MeV, $E = 33, 36, and 38$ MeV; ${}^{28}{Si}$ ( ${}^{18}O$ , ${}^{18}O$ ) ${}^{28}{Si}$ ( ${}^{18}O$ , ${}^{18}O$ ) ${}^{28}{Si}^{*}$ $Q = - 1.78$ MeV, $E = 36$ MeV, measured $σ (θ)$ , $θ_{lab} = 10 - 70$ ; deduced optical model parameters and nuclear deformation lengths, compared deformation lengths with systematics.

Yrast decay schemes from heavy-ion + ${}^{48}{Ca}$ fusion-evaporation reactions. II. ${}^{59 - 60}{Fe}$ and ${}^{59 - 60}{Co}$

E. K. Warburton, J. W. Olness, A. M. Nathan, J. J. Kolata, and J. B. McGrory

Phys. Rev. C 16, 1027 (1977) - Published 1 September, 1977

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Fusion-evaporation reactions induced by beams of 25-55-Mev ${}^{15}N$ and ${}^{18}O$ on an isotopically enriched ${}^{48}{Ca}$ target have been used to populate high-spin yrast levels in ${}^{59 - 60}{Fe}$ and ${}^{59 - 60}{Co}$ . Measurements consisted of $γ$ -ray excitation functions, angular distributions, $γ - γ$ coincidences, and recoil-distance and Doppler-shift lifetime measurements, from which were deduced the energy levels, $γ$ -ray branching ratios, most probable spin-parity assignments, and level lifetimes. The results of $p - γ$ correlation measurements in the ${}^{58}{Fe} (t, p γ) {}^{60}{Fe}$ reaction are also reported.

NUCLEAR REACTIONS ${}^{48}{Ca} ({}^{15}N, x n, y p) {}^{59, 60}{Fe}$ and ${}^{59 - 60}{Co}$ and ${}^{48}{Ca} ({}^{18}O, x n, z α) {}^{59, 60}{Fe}$ . $E = 25 - 55$ MeV; measured $σ (E, E_{γ})$ and coin; deduced levels; measured $σ (E_{γ}, θ)$ ; deduced $J^{π}$ for high-spin levels; measured RDM and DSA; deduced $τ_{m}$ , ${| M (M 1) |}^{2}$ and ${| M (E 2) |}^{2}$ , ${}^{58}{Fe} (t, p γ) {}^{60}{Fe}$ ; measured $p - γ (θ)$ ; deduced $J^{π}$ . Enriched targets, Ge(Li) detectors.

${}^{13}C ({}^{6}{Li}, α) {}^{15}N$ : Emphasis of back-angle data

L. H. Harwood and K. W. Kemper

Phys. Rev. C 16, 1040 (1977) - Published 1 September, 1977

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The reaction ${}^{13}C ({}^{6}{Li}, α) {}^{15}N$ has been measured at $E ({}^{6}{Li}) = 32$ MeV in the lab angular range from 7.5° to 170° in 2.5° steps. Angular distributions were extracted for states up to 13.02 MeV in excitation. All states showed back-angle enhancements. A Hauser-Feshbach analysis could only explain the back-angle enhancement for the state at 7.57 MeV. For the remaining states, zero-range distorted-wave Bron-approximation calculations with simple wave functions reproduced the trends and magnitudes of the data but were out of phase with the data by 5°. Comparisons of the shape of the angular distributions to the ${}^{16}O ({}^{6}{Li}, α) {}^{18}F$ data indicated that the states at 9.152, 9.83, and 13.02 MeV are two particle-three hole and that the 9.83 MeV state has negative parity.

NUCLEAR REACTIONS ${}^{13}C ({}^{6}{Li}, α)$ , $E = 32.0$ MeV; measured $σ (θ)$ , $θ = 7.5 ° - 170 °$ lab, $Δ θ = 2.5 °$ ; compared data to previous measured ( ${}^{6}{Li}, α$ ) data and to zero-range DWBA and Hauser-Feshbach calculations.

Effect of the finite range of the nuclear force on the dynamics of fission and heavy-ion collisions

Arnold J. Sierk and J. Rayford Nix

Phys. Rev. C 16, 1048 (1977) - Published 1 September, 1977

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We study the effect on dynamical calculations of fission and heavy-ion collisions of replacing the surface energy of the liquid-drop model with a modification that takes into account the lowering of the nuclear macroscopic energy due to the finite range of the nuclear force. This energy is caculated by performing a two-dimensional volume integral over the nuclear density of a two-body attractive Yukawa potential, in analogy with the calculation of the electrostatic energy of a charge distribution. The kinetic energy of the nuclear liquid drop is calculated for incompressible, nearly irrotational hydrodynamical flow by use of the Werner-Wheeler method. The dissipation of collective energy into internal, single-particle excitation energy is neglected. In the case of fission, the liquid-drop model and finite-range model give similar results, although the liquid-drop model predicts a somewhat larger fission-fragment excitation energy. In the case of heavy-ion collisions, the surface energy of the liquid-drop model causes a large coupling of energy from relative center-of-mass motion into higher-degree collective motion. This increases the energy over the onedimensional interaction barrier that is needed to cause compound-nucleus formation in head-on collisions for symmetric systems. For an $A = 250$ compound system, the predicted energy over the barrier is about 170 MeV in the liquid-drop model, as compared to about 40 MeV in the finite-range model. We conclude that the effect of the finite range of the nuclear force is small in calculations of fission, but that it must be included in calculations of heavy-ion collisions.

NUCLEAR REACTIONS, FISSION ${}^{236}U$ , ${}^{300}120$ fission, ${}^{150}{Nd}$ + ${}^{150}{Nd}$ → ${}^{300}120$ . Calculated effect of finite range of nuclear force on collective dynamics. Liquid-drop model, modified liquid-drop model, hydrodynamical model, dynamical trajectory, fission-fragment kinetic energy, energy required for compound-nucleus formation in very-heavy-ion collisions.

Stastical analysis of heavy-ion-induced fission excitation functions

J. Bisplinghoff, A. Mignerey, M. Blann, P. David, and W. Scobel

Phys. Rev. C 16, 1058 (1977) - Published 1 September, 1977

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The Bohr-Wheeler model has been used with the rotating liquid drop model to calculate fission excitation functions using a computer code with multiple particle emission competition. Calculations were performed for fission induced by ${}^{35}{Cl}$ ions with laboratory energies up to 170 MeV on ${}^{62}{Ni}$ , ${}^{116}{Sn}$ , and ${}^{141}\Pr$ targets. The dependence of the fission cross sections on angular momentum, barrier heights, ground state and saddle point level density parameters, and for first versus multiple chance fission is illustrated. One set of parameters, not necessarily unique, is shown which gives fair reproduction of the measured ${}^{116}{Sn}$ and ${}^{141}\Pr$ + ${}^{35}{Cl}$ fission excitation functions. It is shown that fission barriers considerably lower than the rotating liquid drop values are required and that variations of other parameters alone cannot reproduce the experimental excitation functions. Asymptotic weaknesses of the statistical treatment at high excitation energies are discussed and qualitatively shown to give errors in the direction observed in the comparisons of experimental and calculated results.

NUCLEAR REACTIONS ${}^{62}{Ni}$ , ${}^{116}{Sn}$ , ${}^{141}\Pr ({}^{35}{Cl}, f)$ , $E = 155 - 170$ MeV, calculated $σ (E)$ , statistical model.

Direct measurement of prompt neutrons emitted in fission of ${}^{226}{Ra}$ by 12 MeV protons

A. Gayer and Z. Fraenkel

Phys. Rev. C 16, 1066 (1977) - Published 1 September, 1977

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Prompt neutron energy distributions were measured at 0° and 90° with respect to the fission axis, in correlation with the mass-energy distribution of the fragments, for the fission of ${}^{226}{Ra}$ induced by 12 MeV protons. The average number and average kinetic energy of prefission and postfission neutrons were obtained as a function of fragment mass and total kinetic energy. The average number of prefission neutrons emitted is 0.33 ± 0.15 $\frac{n}{fission}$ (this includes also contributions from scission neutrons). By comparing this result with calculations of the average number of "true" prefission neutrons, it was found that the number of true prefission neutrons is zero. The average number of postfission neutrons emitted from both fragments is 3.20 ± 0.20 with an average kinetic energy of 1.33 ± 0.07 MeV. The dependence of the number of postfission neutrons on the fragment mass can be interpreted as a combination of a sawtooth structure for the asymmetric mass division and a linearly increasing function for the symmetric mass division.

NUCLEAR REACTIONS, FISSION ${}^{226}{Ra} (p, x n f)$ , $E = 12$ MeV; measured coin. fragment energy, neutron velocity at $θ = 0 °, 90 °$ with respect to fragment; deduced number and kinetic energy of prefission, postfission neutrons.

Prompt $γ$ rays emitted in fission of ${}^{226}{Ra}$ by 12 MeV protons

A. Gayer and Z. Fraenkel

Phys. Rev. C 16, 1077 (1977) - Published 1 September, 1977

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The total energy associated with the emission of prompt $γ$ rays in fission of ${}^{226}{Ra}$ induced by 12 MeV protons was measured in correlation with the fragment mass and kinetic energy. The dependence of the average total $γ$ ray energy on fragment mass and total kinetic energy resembles the corresponding dependence of the average number of neutrons. Using these results and the results for the average number of neutrons, we calculatd the excitation energy of the fragments at the scission point. The results support the view that the scission-point configuration for the symmetric fission mode is more elongated than that for the asymmetric mode.

NUCLEAR REACTIONS, FISSION ${}^{226}{Ra} (p, f)$ , $E = 12$ MeV; measured coin. fragment energy, $γ$ -ray energy at 0° with respect to fragment; deduced total $γ$ -ray energy emitted from the fission fragments.

Separation of the $Δ Δ$ and $NN$ components of the deuteron by the kinematics of high energy $π D$ reactions

Michael Danos and H. Thomas Williams

Phys. Rev. C 16, 1082 (1977) - Published 1 September, 1977

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The kinematics of the reaction $π + d \to π + N + anything$ is analyzed for 15 GeV incoming pions. It is shown that by observing both the invariant mass and the angular correlations of backward $π N$ events one can insure that the observed particles arise from the decay of a spectator $Δ$ in a quasifree scattering event, i.e., they give a quantitative estimate of the $Δ Δ$ admixture of the deuteron. Failure of experimental observation of such events would indicate a failure of the effective Lagrangian formalism.

NUCLEAR REACTIONS Quasifree scattering, $Δ$ admixture.

Interaction of $K^{+}$ mesons with nuclei

Carl B. Dover and P. J. Moffa

Phys. Rev. C 16, 1087 (1977) - Published 1 September, 1977

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We investigate the general features of $K^{+}$ meson interactions with nucleons and nuclei. A first-order optical potential is constructed, and used to predict $K^{+}$ total elastic and reaction cross sections on typical nuclei in the low-energy domain ( $p_{lab} \leq 800$ MeV/c). The sensitivity of these cross sections to changes in the nuclear radius and surface thickness is explored. Comparisons with the available $K^{+}$ -emulsion data are made. We emphasize that a low-energy $K^{+}$ is the only available strongly interacting hadron which is weakly absorbed in nuclei (mean free path ≅ 7 fm). This makes it an appealingly simple probe for nuclear structure studies.

NUCLEAR REACTIONS $K^{+}$ -nucleus scattering; optical model; Kisslingertype potential.

Inelastic interactions of pions with the complex nuclei of emulsions

S. C. Chakravartty and J. Hébert

Phys. Rev. C 16, 1097 (1977) - Published 1 September, 1977

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Cross sections for inelastic interactions of pions with complex nuclei of emulsion have been measured at various pion energies in the (3,3) resonance energy region. The results have been interpreted in terms of the pion-nucleon interaction cross section through Fraenkel's isobar model using the optical model formalism. A detailed analysis of the stars produced by the positive pions in that energy range was also made and the energy and the opening angle distributions were fitted with those obtained from the Monte Carlo calculations based on the isobar model. Good agreement in each case supports the isobar model for the inelastic interaction of pions in complex nuclei.

NUCLEAR REACTIONS ( $π^{+}, emulsion$ ), $E = 10 - 300$ MeV, measured and calculated $σ (E)$ , $N - E$ distribution, isobar model.

Pion production and absorption in nuclear reactions. I. The vertex function

W. T. Nutt and C. M. Shakin

Phys. Rev. C 16, 1107 (1977) - Published 1 September, 1977

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We have performed a model calculation of the pion-nucleon vertex function for the case in which one nucleon is allowed to go far off its mass shell. We discuss the relevance of this vertex function for the calculation of pion production and absorption in nuclear reactions, such as ( $π^{+}, p$ ), ( $p, π^{+}$ ), and for the pionic disintegration of the deuteron. The model used is based upon an approximation to an exact equation for the vertex function derived from a field-theoretic model with pseudoscalar coupling. Our calculations indicate a strong dependence of the vertex function on the invariant mass of the off-shell nucleon. The results are dominated by the presence of the 1470 MeV, $P_{11}$ resonance.

NUCLEAR REACTIONS Pion production and absorption, calculation of pion-nucleon vertex function.

$0^{-} \leftrightarrow 0^{+}$ beta decay and muon capture in the $A = 16$ nuclei

A. Bottino, G. Ciocchetti, and C. W. Kim

Phys. Rev. C 16, 1120 (1977) - Published 1 September, 1977

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The muon-capture process $μ^{-} + {}^{16}O (0^{+}) \to {}^{16}N^{*} + ν_{μ}$ and the $β$ decay ${}^{16}N^{*} (0^{-}) \to {}^{16}O (0^{+}) + e^{-} + {\bar{ν}}_{e}$ are analyzed in the elementary particle treatment. Theoretical results are shown to be consistent with experiment and do not support any necessity of a significant upward renormalization of the nucleon form factor $g_{P}$ in nuclei as suggested by a previous analysis by Palffy etal. Slight downward renormalization of $g_{P}$ is consistent with experimental data.

NUCLEAR REACTIONS ${}^{16}O (μ, ν_{μ}) {}^{16}N^{*} (0^{-})$ ; calculated capture rate. ${}^{16}N^{*} (0^{-})$ , calculated $β$ -decay rate.

Pion-nucleon vertex function and the Chew-Low model

W. T. Nutt

Phys. Rev. C 16, 1124 (1977) - Published 1 September, 1977

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We provide an interpretation of the cutoff function used in the Chew-Low theory of pion-nucleon scattering. It is shown that this function may be related to the pion-pion interaction which is not explicitly considered in the Chew-Low approach. Using a previously developed model for the pion-nucleon vertes function, we then perform a "parameter-free" Chew-Low calculation which predicts the $P_{33}$ resonance quite well.

NUCLEAR REACTIONS Pion nucleon vertex function, Chew-Low model for pion-nucleon scattering.

Vibrational levels in the 86-neutron nucleus ${}^{150}{Gd}$

D. R. Haenni and T. T. Sugihara

Phys. Rev. C 16, 1129 (1977) - Published 1 September, 1977

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The decay of 3.6-h ${}^{150}{Tb}$ to levels in ${}^{150}{Gd}$ has been studied by $γ$ -ray and conversion-electron spectroscopy. A level scheme is proposed which accounts for all but 35 of the 256 $γ$ rays assigned to this decay. Most of the low-lying levels in ${}^{150}{Gd}$ show a remarkably close correspondence with the predictions of the simple vibrator model. Possible candidates are observed for three-phonon quadrupole states and for the states coupling quadrupole and octupole phonons. The low-lying positive-parity levels can be adequately described by the phenomenological collective model of Gneuss and Greiner. The microscopic boson-expansion model of Kishimoto and Tamura, however, appears to predict ${}^{150}{Gd}$ to be more transitional than the data imply. Systematics of the 86-neutron isotones show increased stability at 64 protons. This can be correlated with the filling of the $g_{\frac{7}{2}}$ and $d_{\frac{5}{2}}$ spherical proton orbitals.

RADIOACTIVITY ${}^{150}{Tb}$ [from ${}^{151}{Eu} ({}^{3}{He}, 4 n)$ ], measured $T_{\frac{1}{2}}$ , $E_{γ}$ , $E_{β +}$ , $I_{γ}$ , $I_{ce}$ , $γ - γ$ , and $β^{+} - γ$ coin; deduced $Q$ , $log ft$ . ${}^{150}{Gd}$ deduced levels, ICC, $J$ , $π$ . Enriched target, Ge(Li), and Si(Li) detectors.

Production, $L$ x-ray identification, and decay of the nuclide ${}^{260}105$

C. E. Bemis, Jr., P. F. Dittner, R. J. Silva, R. L. Hahn, J. R. Tarrant, L. D. Hunt, and D. C. Hensley

Phys. Rev. C 16, 1146 (1977) - Published 1 September, 1977

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The nuclide ${}^{260}105$ has been produced in the ${}^{249}{Cf} ({}^{15}N, 4 n)$ reaction and its decay properties investigated. The $α$ -decay branch of 1.52 ± 0.13-sec ${}^{260}105$ has been measured to be (90.4±0.6)% with spontaneous-fission decay the remainder [(9.6±0.6)%]. Measured $α$ -particle energies and intensities (% per decay) are 9.041±0.014 MeV (48±5), 9.074±0.014 MeV (25±3), and 9.120±0.017 MeV (17±3). Characteristic $L$ series x rays of element 103 were observed in coincidence with these $α$ -particle groups, thus providing elemental identification. The ${}^{256}{Lr}$ $α$ -decay daughter was observed in a direct time-correlated genetic linkage, thus providing the mass number assignment. The absence of characteristic $L$ - or $K$ -series x rays of element 104 in time coincidence with, but preceding, spontaneous-fission-decay events, has allowed an upper limit of 2.5% to be placed on the electron-capture decay branch of ${}^{260}105$ to the elusive nuclide 0.1-sec ${}^{260}104$ . If ${}^{260}104$ is a spontaneous-fission emitter with a half-life ≤ 100 μsec, as some predictions would indicate, then the electron-capture decay branch of ${}^{260}105$ is μ0.2%.

RADIOACTIVITY ${}^{260}105$ [from ${}^{249}{Cf} ({}^{15}N, 4 n)$ reaction]; measured $t_{\frac{1}{2}}$ , $E_{α}$ , $I_{α}$ , $E_{SF}$ , $E_{SF}$ , $I_{EC}$ , $E_{X}$ , $L_{X}$ , $E_{γ}$ , $I_{γ}$ ; $α - X$ coin. and $SF - X$ coin. $α - α$ time correlation; deduced ${}^{256}{Lr}$ levels, $J$ , $K$ , $π α$ hindrance, SF hindrance, atomic number mass number. Enriched target.

Charge-dependent and $A$ -dependent effects in isotope shifts of Coulomb displacement energies

R. Sherr

Phys. Rev. C 16, 1159 (1977) - Published 1 September, 1977

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Coulomb displacement energies in a series of isotopes generally decrease with $A$ . This decrease can arise from an increase with $A$ of the average distance of interaction between pairs of protons. In the shell model a decrease can also result from charge-independence-breaking effects if the neutron-proton interaction for the valence nucleons is more attractive than the neutron-neutron interaction. Using the model recently proposed by Sherr and Talmi for the $1 d_{\frac{3}{2}}$ shell, existing data for this shell and also the $1 d_{\frac{5}{2}}$ and $1 f_{\frac{7}{2}}$ shells were analyzed allowing all matrix elements to vary as $A^{- \frac{λ}{3}}$ . Least squares calculations of the rms deviation $σ$ were carried out for varying values of $λ$ from -2 to +2. It was found that although there was a minimum in $σ$ vs $λ$ it was too shallow to exclude any $λ$ for -1 to +1 in the $1 d_{\frac{3}{2}}$ and $1 f_{\frac{7}{2}}$ shells or 0 to +1 in the $1 d_{\frac{5}{2}}$ shell. It is therefore not possible to distinguish between $A$ dependence and charge dependence in this model. The magnitude of the latter as expressed in terms of $np - nn$ matrix elements depends strongly on the former. As $λ$ increases from -1 to +1, these $np - nn$ matrix elements decrease roughly linearly in absolute magnitude and eventually change sign. For $λ = 0$ they have appreciable and reasonable magnitudes for the $1 d_{\frac{3}{2}}$ and $1 f_{\frac{7}{2}}$ shells but for the $1 d_{\frac{5}{2}}$ shell the values are too small to be considered significant.

NUCLEAR STRUCTURE Shell model analysis of Coulomb displacement energies in ground state multiplets in $1 d_{\frac{5}{2}}$ , $1 d_{\frac{3}{2}}$ , and $1 f_{\frac{7}{2}}$ shells.

Connection between the Migdal and surface $δ$ interactions

S. A. Moszkowski and Y. R. Waghmare

Phys. Rev. C 16, 1176 (1977) - Published 1 September, 1977

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The forms and parameters of the spin-isospin averaged Migdal and surface $δ$ interactions are derived. It is shown that in a simple example for the density distribution of the valence nucleons, the two interactions yield the same angle-averaged interaction energies.

NUCLEAR STRUCTURE Derivation of parameters of Migdal interaction and comparison with surface $δ$ interaction.

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Recent Articles

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Recent Issues

Erratum: 28- and 34-MeV ${}^{6}{Li}$ and ${}^{7}{Li}$ elastic scattering on nuclei with $40 \leq A \leq 91$

Gamma rays from thermal neutron capture in ${}^{136}{Xe}$

Isotope and element distributions of the evaporation residues from fusion of 160 MeV ${}^{32}S$ with ${}^{24, 25, 26}{Mg}$ and ${}^{27}{Al}$

Nuclear shapes of ${}^{24}{Mg}$ and ${}^{28}{Si}$ by inelastic scattering of ${}^{12}C$ and ${}^{16, 18}O$

Yrast decay schemes from heavy-ion + ${}^{48}{Ca}$ fusion-evaporation reactions. II. ${}^{59 - 60}{Fe}$ and ${}^{59 - 60}{Co}$

${}^{13}C ({}^{6}{Li}, α) {}^{15}N$ : Emphasis of back-angle data

Effect of the finite range of the nuclear force on the dynamics of fission and heavy-ion collisions

Stastical analysis of heavy-ion-induced fission excitation functions

Direct measurement of prompt neutrons emitted in fission of ${}^{226}{Ra}$ by 12 MeV protons

Prompt $γ$ rays emitted in fission of ${}^{226}{Ra}$ by 12 MeV protons

Separation of the $Δ Δ$ and $NN$ components of the deuteron by the kinematics of high energy $π D$ reactions

Interaction of $K^{+}$ mesons with nuclei

Inelastic interactions of pions with the complex nuclei of emulsions

Pion production and absorption in nuclear reactions. I. The vertex function

$0^{-} \leftrightarrow 0^{+}$ beta decay and muon capture in the $A = 16$ nuclei

Pion-nucleon vertex function and the Chew-Low model

Vibrational levels in the 86-neutron nucleus ${}^{150}{Gd}$

Production, $L$ x-ray identification, and decay of the nuclide ${}^{260}105$

Charge-dependent and $A$ -dependent effects in isotope shifts of Coulomb displacement energies

Connection between the Migdal and surface $δ$ interactions

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