Recent Articles

Volume integrals of real part of nucleon optical potentials

S. Kailas and S. K. Gupta

Phys. Rev. C 17, 2236 (1978) - Published 1 June, 1978

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Volume integrals of the real part of the proton and neutron optical potentials are computed using the existing phenomenological analyses for $A = 10 - 238$ . These results are in good agreement with the Jeukenne-Lejeune-Mahaux model which employs Reid's hard core nucleon-nucleon interaction. An empirical expression having an isovector dependence has been used to fit the volume integrals and the isovector component of the real potential has been estimated.

NUCLEAR REACTIONS Optical potential of Jeukenne, Lejeune, and Mahaux for finite nuclei. Volume integrals of real part of nucleon optical potentials.

Reply to "Comments on alternate formulations for preequilibrium decay"

E. Gadioli, E. Gadioli Erba, and G. Tagliaferri

Phys. Rev. C 17, 2238 (1978) - Published 1 June, 1978

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Blann's criticisms of the exciton model formulation are found to originate mainly in misunderstandings. An attempt is made to support the contention that the exciton model uses a correct quantum statistical approach to the problem of preequilibrium decay.

NUCLEAR STRUCTURE Exciton model, precompound decay.

RAPID COMMUNICATION

Volume versus surface sampling of Maxwellian distributions in nuclear reactions

Alfred S. Goldhaber

Phys. Rev. C 17, 2243(R) (1978) - Published 1 June, 1978

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The pre-exponential factor in a thermal distribution of classical particles depends on whether the particles have been emitted from the surface of a hot body or are contained in a volume of gas of given temperature. Precisely the appropriate factors describe nuclear evaporation of very low energy neutrons (volume sampling) or moderate energy fragments (surface), as well as the high energy processes of projectile fragmentation and "fireball" breakup (volume).

NUCLEAR REACTIONS Thermal distributions of products; pre-exponential factors; thermal neutrons, $\sqrt{E}$ ; evaporation particles, $E$ ; fragmentation or breakup, $\sqrt{E}$ .

RAPID COMMUNICATION

Optimum $Q$ value in heavy-ion-induced neutron transfer at the Coulomb barrier

W. Henning, Y. Eisen, H.-J. Körner, D. G. Kovar, J. P. Schiffer, S. Vigdor, and B. Zeidman

Phys. Rev. C 17, 2245(R) (1978) - Published 1 June, 1978

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The optimum $Q$ value for the ${}^{118}{Sn}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{120}{Sn}$ two-neutron transfer reaction was measured near the Coulomb barrier as a function of incident energy and scattering angle. The experimental results are not reproduced in a satisfactory manner by semiclassical predictions, and only approximately by distorted-wave Born approximation.

NUCLEAR REACTIONS ${}^{118}{Sn}$ ( ${}^{18}O$ , ${}^{16}O$ ) ${}^{120}{Sn}$ , $53 MeV \leq E \leq 62 MeV$ , measured $σ (θ, E)$ ; deduced $Q_{opt}$ .

RAPID COMMUNICATION

Excitation functions and Legendre analysis for the ${}^{12}C$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{16}O$ (g.s.) reaction

D. R. James and N. R. Fletcher

Phys. Rev. C 17, 2248(R) (1978) - Published 1 June, 1978

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Additional excitation functions for ${}^{12}C$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{16}O$ (g.s.) have been measured. A Legendre analysis of $σ (θ, E)$ confirms previous $J^{π}$ assignments of resonant structures and identifies new ones. A fragmentation of giant quasimolecular resonances provides a preferable interpretation of the resonance phenomena observed.

NUCLEAR REACTIONS ${}^{12}C$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{16}O$ (g.s.), measured $σ (θ, E)$ , $E_{c . m .} ≃ 9 to 20$ MeV, deduced $J^{π}$ of resonances.

RAPID COMMUNICATION

Masses of ${}^{121, 123, 125}I$ and energy levels of the highly neutron-deficient ${}^{121}I$

A. Szanto de Toledo, H. V. Klapdor, W. Saathoff, E. M. Szanto, and M. Schrader

Phys. Rev. C 17, 2253(R) (1978) - Published 1 June, 1978

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The mass excesses of the nuclides ${}^{121, 123, 125}I$ have been determined to be - 86288.0 ± 21.4 keV, - 87934.3 ± 5.3 keV, and - 88837.9 ± 4.8 keV, respectively, by measuring $Q$ values of the reactions ${}^{120 - 130}{Te} ({}^{3}{He}, d)$ and ${}^{124 - 130}{Te} (α, t)$ with a quadrupole-dipole-dipole-dipole magnetic spectrograph. Furthermore, 26 new enery levels in ${}^{121}I$ have been determined.

NUCLEAR REACTIONS ${}^{120 - 130}{Te} ({}^{3}{He}, d)$ , ${}^{124 - 130}{Te} (α, t)$ , $E = 36$ MeV, measured $Q$ values, mass excesses, level scheme of ${}^{121}I$ .

RAPID COMMUNICATION

Influence of low-lying collective states on the elastic scattering of heavy ions below the Coulomb barrier

G. Baur, F. Rösel, and D. Trautmann

Phys. Rev. C 17, 2256(R) (1978) - Published 1 June, 1978

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The elastic scattering of heavy ions in the sub-Coulomb region is calculated in the semiclassical Coulomb excitation theory. These results are compared to a recently developed optical model calculation. We investigate the importance of higher order terms, which could not be taken into account in the optical model approach.

NUCLEAR REACTIONS Calculation of the elastic scattering of heavy ions below the Coulomb barrier. Investigation of the importance of higher order effects and comparison with a recently developed local optical potential model.

Erratum: ${}^{10}B$ -induced $2 n$ and $2 p$ transfer reactions on light targets

M. Hamm and K. Nagatani

Phys. Rev. C 17, 2258 (1978) - Published 1 June, 1978

Core excited $T = 2$ levels in $A = 12$ from studies of ${}^{12}{Be}$

D. E. Alburger, D. P. Balamuth, J. M. Lind, L. Mulligan, K. C. Young, Jr., R. W. Zurmühle, and R. Middleton

Phys. Rev. C 17, 1525 (1978) - Published 1 May, 1978

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Levels of ${}^{12}{Be}$ have been studied using the ${}^{10}{Be} (t, p) {}^{12}{Be}$ reaction. The spin of an excited state at $E_{x} = 2.110 \pm 0.015$ MeV is determined model independently as $J = 2$ using a measurement of the proton- $γ$ angular correlation in an axially symmetric geometry. A mechanically chopped beam was used to study $β$ activity following the irradiation of ${}^{10}{Be}$ by 12 MeV tritons. A least squares analysis of the resulting decay curve yields $T_{\frac{1}{2}} ({}^{12}{Be}) = 24.4 \pm 3.0$ msec. A ${}^{3}{He}$ neutron detector was used to search for delayed neutrons; a 1σ upper limit on a delayed neutron branch of 1% is obtained. The above results support the suggestion that low-lying states in ${}^{12}{Be}$ involve the excitation of particles into the $1 s - 0 d$ shell.

NUCLEAR REACTIONS ${}^{10}{Be} (t, p γ)$ , $E = 12$ MeV measured $σ (E_{p})$ , $p γ (θ)$ , $E_{γ}$ . ${}^{12}{Be}$ deduced levels, $J$ , $π$ . Enriched target.

RADIOACTIVITY ${}^{12}{Be}$ [from ${}^{10}{Be} (t, p)$ ]; measured $T_{\frac{1}{2}}$ from $β$ activity. Searched for delayed neutrons.

Electrodisintegration of ${}^{12}C$

F. J. Kline and Evans Hayward

Phys. Rev. C 17, 1531 (1978) - Published 1 May, 1978

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The cross section for the production of the ${}^{11}C$ activity by bombarding ${}^{12}C$ with 30 MeV electrons has been measured absolutely. The result, 11.9 ± 0.2 μb, has a smaller absolute error than any previous measurement. This value corresponds to a ( $γ, n$ ) cross section integrated to 30 MeV of 41.0 ± 0.6 MeV mb, based on a distorted-wave Born-approximation electric dipole virtual photon spectrum.

NUCLEAR REACTIONS ${}^{12}C (e, n)$ , $F_{e} = 30$ MeV, $σ (e, n)$ measured absolutely.

Mass of lowest $T = 2$ state of ${}^{12}C$

R. G. H. Robertson, T. L. Khoo, G. M. Crawley, A. B. McDonald, E. G. Adelberger, and S. J. Freedman

Phys. Rev. C 17, 1535 (1978) - Published 1 May, 1978

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A precise measurement of the excitation energy of the lowest $T = 2$ state in ${}^{12}C$ has been made via the ${}^{14}C (p, t) {}^{12}C$ reaction. The value obtained, 27.5950 ± 0.0024 MeV, is in agreement with earlier (less precise) measurements and therefore does not explain the failure to observe the $T = 2$ state in isospin-forbidden resonance reactions. Also reported in this work are an upper limit of 30 keV for the total width of the $T = 2$ state and an excitation energy of 3.3492 ± 0.0012 MeV for the first excited state of ${}^{10}C$ .

NUCLEAR REACTIONS ${}^{14}C (p, t)$ , $E_{x} = 27.6$ MeV, measured $Q$ , $Γ$ . ${}^{12}C (p, t)$ , $E_{x} = 3.35$ , measured $Q$ . Magnetic spectrograph.

Complex-particle emission in the pre-equilibrium exciton model

J. R. Wu and C. C. Chang

Phys. Rev. C 17, 1540 (1978) - Published 1 May, 1978

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The complex-particle ( $A \leq 4$ ) emission in the particle induced reaction was analyzed in the pre-equilibrium reaction mechanism. A simple closed form pre-equilibrium exciton model is employed. The complex particle is assumed to form with a certain formation probability from the excited particles (protons and neutrons) which correlate to each other with the right combination of proton and neutron numbers and the momentum in order to form a cluster. The complex-particle formation probability extracted from the proton induced reactions on several nuclei from ${}^{12}C$ to ${}^{209}{Bi}$ shows strong $A$ dependence.

NUCLEAR REACTIONS ${}^{12}C$ , ${}^{16}O$ , ${}^{27}{Al}$ , ${}^{54}{Fe}$ , ${}^{89}Y$ , ${}^{120}{Sn}$ , ${}^{197}{Au}$ , ${}^{209}{Bi} (p, x)$ , $E_{p} = 62$ MeV; ${}^{54}{Fe} (p, x)$ ; $E_{p} = 29 and 39$ MeV, ${}^{58}{Ni} (p, x)$ , $E_{p} = 90$ MeV; pre-equilibrium exciton model.

( $p, γ$ ) resonance strengths in the $s - d$ shell

B. M. Paine, S. R. Kennett, and D. G. Sargood

Phys. Rev. C 17, 1550 (1978) - Published 1 May, 1978

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Resonance strengths of selected resonances in the range $E_{p} = 0.5 - 0.9$ MeV in the ( $p, γ$ ) reactions on ${}^{23}{Na}$ , ${}^{27}{Al}$ , ${}^{31}P$ , and ${}^{35}{Cl}$ have been compared through relative yield measurements with targets consisting of mixtures of chemical compounds, each containing at least two of the isotopes of interest. Chemical composition of the targets was determined by Rutherford scattering of $α$ particles. Absolute strengths were deduced by normalizing to a strength of $S = 3.26 \pm 0.4$ eV for the $E_{p} = 633$ keV resonance in ${}^{27}{Al} (p, γ) {}^{28}{Si}$ .

NUCLEAR REACTIONS ${}^{23}{Na}$ , ${}^{27}{Al}$ , ${}^{31}P$ , ${}^{35}{Cl} (p, γ)$ , $E = 0.5 - 0.9$ MeV; measured $σ (E_{p})$ . Deduced resonance strengths. Natural targets.

Structure of ${}^{116}{Sb}$ Studied with the ${}^{115}{Sn} ({}^{3}{He}, d) {}^{116}{Sb}$ reaction

R. Kamermans, J. van Driel, H. P. Blok, and P. J. Blankert

Phys. Rev. C 17, 1555 (1978) - Published 1 May, 1978

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The ${}^{115}{Sn} ({}^{3}{He}, d) {}^{116}{Sb}$ reaction was performed to obtain a more sensitive test of two quasiparticle calculations for ${}^{116}{Sb}$ . These calculations gave a good description of the excitation energies and partial halflives of the low lying states of ${}^{116}{Sb}$ . Good agreement between measured and calculated spectroscopic factors is found. The calculated low lying $J^{π} = 0^{+}$ state ( $E_{x} = 420$ keV) which has not been observed so far should be strongly excited in this reaction. However, no indication is found for such a state below $E_{x} = 1200$ keV.

NUCLEAR REACTIONS ${}^{115, 116}{Sn} ({}^{3}{He}, d)$ , $E = 28.4$ MeV, measured $σ (θ)$ . ${}^{116, 117}{Sb}$ deduced levels, $J$ , $π$ , $S$ , DWBA analysis, magnetic spectrograph, enriched target.

${}^{192}{Pt} (α, α^{'})$ reaction at $E = 24$ MeV

F. Todd Baker, Alan Scott, R. M. Ronningen, T. H. Kruse, R. Suchannek, and W. Savin

Phys. Rev. C 17, 1559 (1978) - Published 1 May, 1978

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Angular distributions for excitation of the $0^{+}$ , $2^{+}$ , $2^{+'}$ , $4^{+}$ , $4^{+'}$ , and $3^{-}$ states in ${}^{192}{Pt}$ by 24 MeV $α$ particles have been measured. Coupled-channels analysis of the ground-state band yields negative $β_{4}$ deformations. Analysis of the " $γ$ band" yields a negative $E 2$ interference term $P_{3}$ and a surprising large direct $E 4$ excitation of the $4^{+'}$ state.

NUCLEAR REACTIONS ${}^{192}{Pt} (α, α^{'})$ , $E_{α} = 24$ MeV; measured $σ (θ, E_{α}^{'})$ ; deduced Coulomb and nuclear deformations $β_{2}$ , $β_{4}$ , $β_{3}$ , and relative signs of matrix elements. Enriched target. Coupled-channels analysis.

Levels in ${}^{189}{Ir}$ and ${}^{191}{Ir}$ observed in the ( $p, t$ ) reaction

Gordon L. Struble, Robert G. Lanier, Lloyd G. Mann, Raymond K. Sheline, Richard T. Kouzes, William H. Moore, Dennis Mueller, Robert A. Naumann, and Ivan C. Oelrich

Phys. Rev. C 17, 1564 (1978) - Published 1 May, 1978

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Levels in ${}^{189}{Ir}$ and ${}^{191}{Ir}$ were populated by the ( $p, t$ ) reaction, using 34-MeV protons and isotopically enriched ${}^{191}{Ir}$ and ${}^{193}{Ir}$ targets. A number of low-lying positive-parity bands were observed. In addition the 11/ $2^{-}$ [505] bandhead was also weakly populated. The 3/2 1/ $2^{+}$ [400] states in ${}^{189}{Ir}$ and ${}^{191}{Ir}$ have similar but anomalous angular distributions. Four strongly populated states with $L = 0$ angular distributions are observed from 719 to 1261 keV in ${}^{189}{Ir}$ . For the same energy region in ${}^{191}{Ir}$ , the $L = 0$ states are less strongly populated.

NUCLEAR REACTIONS ${}^{191}{Ir} (p, t)$ and ${}^{193}{Ir} (p, t)$ , $E_{lab} = 34.7$ MeV; measured $σ (θ)$ ; deduced $E_{x}$ , $L$ , $J^{π}$ of ${}^{189}{Ir}$ and ${}^{191}{Ir}$ levels.

Mass and low-lying levels of ${}^{67}{Ge}$ ; trends in the structure of ${}^{63, 65}{Ni}$ , ${}^{65, 67}{Zn}$ , and ${}^{67, 69}{Ge}$

M. J. Murphy, C. N. Davids, E. B. Norman, and R. C. Pardo

Phys. Rev. C 17, 1574 (1978) - Published 1 May, 1978

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${}_{32}^{67}{Ge}_{35}$ has been studied via the reaction ${}^{64}{Zn} (α, n γ) {}^{67}{Ge}$ . The mass excess was measured to be -62666 ± 12 keV, and four low-lying excited states have been identified. Among these newly identified levels is an isomeric state at 18.2 keV having a measured total mean lifetime of 18.5 ± 0.3 μs and a measured $K$ -shell internal conversion coefficient $α_{K} = 176 \pm 29$ . In addition, the total lifetime of the 63.4 keV isomeric level in ${}^{65}{Ni}$ has been measured to be 104.9 ± 7.1 μs. The level schemes of the six nuclei ${}^{63, 65}{Ni}$ , ${}^{65, 67}{Zn}$ , and ${}^{67, 69}{Ge}$ are then compared, and similarities in their structure and in the decay characteristics of the isomeric states of each are discussed and interpreted in terms of a simple pairing model.

NUCLEAR REACTIONS ${}^{64}{Zn} (α, n γ)$ ; ${}^{67}{Ge}$ mass, level scheme, isomeric level, $E_{γ}$ , $I_{γ}$ , isomeric $T_{\frac{1}{2}}$ , internal conversion coefficient $α_{K}$ . ${}^{64}{Ni} (d, p γ)$ ; ${}^{65}{Ni}$ isomeric level, isomeric $T_{\frac{1}{2}}$ , $E_{γ}$ . Ge(Li) and Si(Li) detectors, enriched targets, pulsed beam. Shell-model calculations; quasiparticle calculation.

Isobaric analog resonances in the ${}^{68}{Zn} (p, γ) {}^{69}{Ga}$ reaction

K. Ramavataram, C. Rangacharyulu, I. M. Szöghy, R. Hilko, and C. St.-Pierre

Phys. Rev. C 17, 1583 (1978) - Published 1 May, 1978

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Isobaric analog resonances in ${}^{69}{Ga}$ corresponding to the ground (1/ $2^{-}$ ) and first excited (9/ $2^{+}$ ) parent states of ${}^{69}{Zn}$ have been studied by the ${}^{68}{Zn} (p, γ)$ reaction. The $γ$ decay of the ground state of ${}^{69}{Zn}$ is compared with the $β$ decay of the parent isobaric analog state. The latter is a pure Gamow-Teller transition to the ground (3/ $2^{-}$ ) and third (3/ $2^{-}$ ) excited states, while both Gamow-Teller and Fermi matrix elements can contribute in the decay to the second excited (1/ $2^{-}$ ) state of ${}^{69}{Ga}$ . The $M 1$ decay widths obtained from the $γ$ decay of the $J^{π} = {\frac{1}{2}}^{-}$ isobaric analog state are in good agreement with the widths extracted from the $log ft$ values in the first two of the three $β$ -decay branches. However, the $M 1$ decay width to the third excited state disagrees with the value deduced from the $log ft$ value of the $β$ decay of the ${}^{69}{Zn}$ g.s. to this state. In addition, the $M 1$ transition strength of the 9/ $2^{+}$ ( $T_{>}$ ) state to the ${9 / 2}^{+}$ ( $T_{<}$ ) state in ${}^{69}{Ga}$ has been measured and is compared with the recently published systematic trends for the analog to antianalog transition in other $f - p$ shell nuclei.

NUCLEAR REACTIONS ${}^{68}{Zn} (p, γ)$ , $E = 3.2 - 3.8$ MeV. ${}^{69}{Ga}$ deduced resonances, measured $E_{γ}$ and $Γ_{γ}$ , $M 1$ strength.

$γ$ decay and splitting of the first analog state in ${}^{53}{Mn}$ , ${}^{55}{Co}$ , and ${}^{59}{Cu}$

J. P. Schapira, J. M. Maison, M. N. Rao, S. Fortier, S. Galès, and H. Laurent

Phys. Rev. C 17, 1588 (1978) - Published 1 May, 1978

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The $γ$ decay of the $2 p_{\frac{3}{2}}$ analog state in ${}^{53}{Mn}$ , ${}^{55}{Co}$ , and ${}^{59}{Cu}$ has been studied at 18 MeV by means of the ( ${}^{3}{He}, d γ$ ) reaction. The $γ$ rays in coincidence with deuterons emitted near 0° were detected by two Ge(Li) detectors located at $θ = 90 ° and 147 °$ . Decay schemes, energies, and spins have been established. The $2 p_{\frac{3}{2}}$ analog state in ${}^{53}{Mn}$ is located at $E_{x} = 6971$ keV. We confirm that the $2 p_{\frac{3}{2}}$ analog state is split in ${}^{55}{Co}$ ( $E_{x} = 4722 and 4747$ keV) and in ${}^{59}{Cu}$ ( $E_{x} = 3885 and 3904$ keV) implying a strong Coulomb mixing with a nearby $T_{<}$ level. We do not see the large reduction of the $M 1$ analog-antianalog transition previously observed in other nuclei in the $f - p$ shell region. Calculations have been completed in a schematic model. Other levels and particularly $1 f_{\frac{5}{2}}$ and $2 p_{\frac{1}{2}}$ analog states in the same nuclei are also observed and discussed.

NUCLEAR REACTIONS ${}^{52}{Cr}$ , ${}^{54}{Fe}$ , ${}^{58}{Ni} ({}^{3}{He}, d γ)$ , $E = 18$ MeV; $γ$ -decay schemes and splitting of the $2 p_{\frac{3}{2}}$ analog state in ${}^{53}{Mn}$ , ${}^{55}{Co}$ , and ${}^{59}{Cu}$ ; Ge(Li) detectors; natural and enriched targets.

Analysis of ${}^{136}{Xe} (p, p_{1})$ on analog resonances and the structure of ${}^{137}{Xe}$

J. L. Foster, Jr., F. Krmpotic, and T. V. Ragland

Phys. Rev. C 17, 1602 (1978) - Published 1 May, 1978

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Analysis of proton inelastic scattering through analog resonances in ${}^{137}{Cs}$ is carried out by the addition of a resonant scattering matrix to a coupled-channel scattering matrix. Neutron coupling to the $2_{1}^{+}$ excited state of ${}^{136}{Xe}$ in wave functions of the parent states in ${}^{137}{Xe}$ is thus determined. For low lying levels, the parentage coefficients extracted from experimental data are in general agreement with calculations performed using the particle-vibrator coupling model.

NUCLEAR REACTIONS ${}^{136}{Xe} (p, p^{'})$ ; $E = 10.26 - 11.82$ MeV; analyzed $σ (E_{p}, θ)$ ; ${}^{137}{Cs}$ IAR deduced $Γ$ , parentage coefficients; ${}^{137}{Xe}$ calculated neutron parentage, levels.

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Recent Issues

Volume integrals of real part of nucleon optical potentials

Reply to "Comments on alternate formulations for preequilibrium decay"

Volume versus surface sampling of Maxwellian distributions in nuclear reactions

Optimum $Q$ value in heavy-ion-induced neutron transfer at the Coulomb barrier

Excitation functions and Legendre analysis for the ${}^{12}C$ ( ${}^{12}C$ , ${}^{8}{Be}$ ) ${}^{16}O$ (g.s.) reaction

Masses of ${}^{121, 123, 125}I$ and energy levels of the highly neutron-deficient ${}^{121}I$

Influence of low-lying collective states on the elastic scattering of heavy ions below the Coulomb barrier

Erratum: ${}^{10}B$ -induced $2 n$ and $2 p$ transfer reactions on light targets

Core excited $T = 2$ levels in $A = 12$ from studies of ${}^{12}{Be}$

Electrodisintegration of ${}^{12}C$

Mass of lowest $T = 2$ state of ${}^{12}C$

Complex-particle emission in the pre-equilibrium exciton model

( $p, γ$ ) resonance strengths in the $s - d$ shell

Structure of ${}^{116}{Sb}$ Studied with the ${}^{115}{Sn} ({}^{3}{He}, d) {}^{116}{Sb}$ reaction

${}^{192}{Pt} (α, α^{'})$ reaction at $E = 24$ MeV

Levels in ${}^{189}{Ir}$ and ${}^{191}{Ir}$ observed in the ( $p, t$ ) reaction

Mass and low-lying levels of ${}^{67}{Ge}$ ; trends in the structure of ${}^{63, 65}{Ni}$ , ${}^{65, 67}{Zn}$ , and ${}^{67, 69}{Ge}$

Isobaric analog resonances in the ${}^{68}{Zn} (p, γ) {}^{69}{Ga}$ reaction

$γ$ decay and splitting of the first analog state in ${}^{53}{Mn}$ , ${}^{55}{Co}$ , and ${}^{59}{Cu}$

Analysis of ${}^{136}{Xe} (p, p_{1})$ on analog resonances and the structure of ${}^{137}{Xe}$

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