Recent Articles

Back-angle anomalies in ${}^{6}{Li}$ scattering from ${}^{40}{Ca}$ and ${}^{44}{Ca}$

H. Bohn, K. A. Eberhard, R. Vandenbosch, K. G. Bernhardt, R. Bangert, and Y.-d. Chan

Phys. Rev. C 16, 665 (1977) - Published 1 August, 1977

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Angular distributions for the elastic and inelastic scattering of 30 MeV ${}^{6}{Li}$ ions from ${}^{40}{Ca}$ and ${}^{44}{Ca}$ have been measured. At backward angles (110°-180°) the cross sections for both elastic and inelastic scattering are an order of magnitude larger for ${}^{6}{Li}$ + ${}^{40}{Ca}$ than for ${}^{6}{Li}$ + ${}^{44}{Ca}$ . The results are compared with the anomalies observed in $α$ and ${}^{3}{He}$ scattering. The difference between the back-angle scattering for ${}^{40}{Ca}$ and ${}^{44}{Ca}$ is discussed in terms of the relative number of competing direct reaction channels capable of carrying away large amounts of angular momentum.

NUCLEAR REACTIONS ${}^{40, 44}{Ca}$ ( ${}^{6}{Li}$ , ${}^{6}{Li}$ ), ( ${}^{6}{Li}$ , ${}^{6}{Li}$ ′), $E = 30$ MeV; measured $σ (E, θ)$ ; calculated $σ (E, θ)$ , optical model, coupled-channel, Hauser-Feshbach calculations.

Comparison of light- and heavy-ion emission from the ${}^{12}C$ + ${}^{16}O$ system

S. L. Tabor, Y. Eisen, D. G. Kovar, and Z. Vager

Phys. Rev. C 16, 673 (1977) - Published 1 August, 1977

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Excitation functions of the total proton and $α$ -particle yields from the ${}^{12}C$ + ${}^{16}O$ reaction have been measured in the range $E_{c . m .} = 12.9 to 27.4$ MeV, with angular distribution measurements at $E_{c . m .} = 14.9, 21, and 26.6$ MeV. For comparison, the elemental distribution of evaporation residues was also measured at the latter three energies. The $α$ excitation curve exhibits structure corresponding to the oscillations seen in an earlier measurement of the total fusion cross section, while the proton cross section increases rather smoothly with energy. At 15 MeV all the proton and $α$ cross section is accounted for by the observed evaporation residues, but an increasing excess of light-ion production is seen at the higher energies. The excess cross section, if interpreted as $3 α$ production, compensates for the previously observed decrease in fusion cross section below the expected total reaction cross section.

NUCLEAR REACTIONS ${}^{12}C ({}^{16}O, p)$ , ${}^{12}C ({}^{16}O, α)$ , $E_{lab} = 30 - 64$ MeV, measured $σ (θ, E)$ ; ${}^{12}C ({}^{16}O, x)$ , $E_{lab} = 35, 49, 62$ MeV, measured $σ (θ, Z)$ .

Magnetic moment and lifetime of the first excited state of mirror nuclei ${}^{21}{Ne}$ and ${}^{21}{Na}$

F. A. Beck, T. Byrski, G. J. Costa, and J. P. Vivien

Phys. Rev. C 16, 679 (1977) - Published 1 August, 1977

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The magnetic moment and lifetime of the first excited states of the mirror nuclei ${}^{21}{Ne}$ and ${}^{21}{Na}$ have been measured by the plunger-time differential-recoil-into-vacuum technique. The states were populated by the ${}^{4}{He} ({}^{18}O, n) {}^{21}{Ne}$ and ${}^{10}B ({}^{16}O, α n) {}^{21}{Na}$ reactions at beam energies such that mainly three-electron recoil ions were produced. Values $| g | = 0.28 \pm 0.03$ and $| g | = 1.48 \pm 0.10$ have been deduced for the ${}^{21}{Ne}$ and ${}^{21}{Na}$ $g$ factors. The mean lifetimes of these states have been determined as $τ = 10.1 \pm 0.3$ ps and $τ = 9.9 \pm 0.4$ ps, respectively. The analysis of the measurements also provides information on atomic state populations in two, three, and four electron systems.

NUCLEAR REACTIONS ${}^{4}{He} ({}^{18}O, n)$ , $E = 19$ MeV; ${}^{10}B ({}^{16}O, α n)$ , $E = 42$ MeV; ${}^{2}H ({}^{20}{Ne}, n)$ , $E = 14$ MeV; measured $γ (θ, t)$ Doppler shift. ${}^{21}{Ne}$ , 350 keV level and ${}^{21}{Na}$ , 332 keV level, deduced $T_{\frac{1}{2}}$ , $| g |$ , ionic electron configurations.

Reactions of ${}^{237}{Np}$ with ${}^{4}{He}$ near the interaction barrier

S. Y. Lin and John M. Alexander

Phys. Rev. C 16, 688 (1977) - Published 1 August, 1977

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Cross sections have been measured for the reactions ${}^{237}{Np} ({}^{4}{He}, f)$ , ( ${}^{4}{He}, n$ ), ( ${}^{4}{He}, 2 n$ ) at energies below the interaction barrier (17.5-22.5 MeV). The total reaction cross sections have been fitted to an equation for theoretical barrier penetration and parameters describing the interaction barrier have been obtained.

NUCLEAR REACTIONS, FISSION ${}^{237}{Np} ({}^{4}{He}, f)$ , ( ${}^{4}{He}, n$ ), ( ${}^{4}{He}, 2 n$ ); $E = 17.5 - 22.5$ MeV; measured $σ (E)$ .

Fission and neutron emission in the actinides at excitation energies of 10-35 MeV

Jacob Gilat, Alain Fleury, Hugues Delagrange, and John M. Alexander

Phys. Rev. C 16, 694 (1977) - Published 1 August, 1977

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The statistical model description of fission through a double humped barrier has been extended from 12 to ≅35 MeV. Calculations have been compared with measured cross sections for ${}^{237}{Np} ({}^{4}{He}, x n)$ reactions giving evaporation residues and fission isomers. A generally good fit to the data has been obtained with level densities from theory and fission barriers that give good fits to the direct reaction fission probabilities at low energies (≤ 12 MeV). In detail there are some significant differences between calculation and experiment. We have explored the sensitivity to the various parameters but have not suggested major redefinitions of level densities, second barriers, and/or isomer masses. The effect of preequilibrium mechanisms has been estimated via the hybrid model of Blann et al. These effects are small for energies at or below the excitation function peaks, but they dominate at high energies. The hybrid model seems to predict too many very high energy neutrons.

NUCLEAR REACTIONS, FISSION $σ (E)$ for ${}^{237}{Np} ({}^{4}{He}, x n)$ reactions as competitors with fission; calculations using double humped fission barrier for $E^{*} <~ 35$ MeV.

Fission probability calculations for heavy-ion induced reactions

Hugues Delagrange, Alain Fleury, and John M. Alexander

Phys. Rev. C 16, 706 (1977) - Published 1 August, 1977

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The Bohr-Wheeler formalism for nuclear fission has been included in a nuclear evaporation code. The added parameters are the saddle-point level density $a_{f}$ and the fission barrier for $J = 0, B_{f}$ . Effects of ${}^{4}{He}$ evaporation are explored by variation of the relevant level density parameter $a_{α}$ . Good fits to fission excitation functions could be achieved but ambiguity remains due to the entrance channel, i.e., the estimated critical angular momentum and the $α$ evaporation probability. Three different systems have been investigated: ${}^{182}W$ + ${}^{12}C$ → ${}^{194}{Hg}$ , ${}^{175}{Lu}$ + ${}^{12}C$ → ${}^{187}{Ir}$ , and ${}^{174}{Yb}$ + ${}^{12}C$ → ${}^{186}{Os}$ . In this framework the measurement of cross sections for $α$ emission and evaporation residues, as well as that for fission, would suffice to fix the important parameters.

NUCLEAR REACTIONS, FISSION ${}^{182}W ({}^{12}C, f)$ ; ${}^{175}{Lu} ({}^{12}C, f)$ ; ${}^{174}{Yb} ({}^{12}C, f)$ ; calculated fission excitation functions; dependence on $l_{crit}$ , $\frac{a_{f}}{a_{n}}$ , $\frac{a_{α}}{a_{n}}$ , $B_{f}$ .

Kinetic-energy distributions in the reactor neutron fission of ${}^{232}U$ and thermal neutron fission of ${}^{241}{Pu}$ and ${}^{245}{Cm}$

A. Ramaswami, Satya Prakash, S. B. Manohar, S. P. Dange, P. P. Venkatesan, and M. V. Ramaniah

Phys. Rev. C 16, 716 (1977) - Published 1 August, 1977

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Recoil ranges of fission products from the reactor neutron fission of ${}^{232}U$ and thermal neutron fission of ${}^{241}{Pu}$ and ${}^{245}{Cm}$ were determined using radiochemical as well as $γ$ spectrometric techniques. Using a semiempirical range-energy equation the recoil ranges were converted into kinetic energies of the fission fragments and hence the kinetic-energy distribution as a function of fragment mass from which the kinetic-energy deficit and the average total kinetic-energy release were obtained. An attempt is made to correlate the variation of the average total kinetic energies in low-energy fission of heavy nuclei with shell structure.

NUCLEAR REACTIONS, FISSION ${}^{232}U$ , ${}^{241}{Pu}$ , ${}^{245}{Cm} (n, f)$ , measured recoil ranges of a number of fission products in aluminium; kinetic-energy deficits and average total kinetic energies are obtained for these systems.

Inverse scattering problem with isobars

J. T. Londergan and E. J. Moniz

Phys. Rev. C 16, 721 (1977) - Published 1 August, 1977

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The inverse scattering problem is solved for a covariant, isobar-dominated scattering amplitude (including inelasticity). Application is made to the $π N P_{33}$ channel, with the $π N Δ$ vertex function and isobar bare mass as results.

NUCLEAR REACTIONS Vertex function and bare mass of $Δ (1232)$ calculated with inverse scattering procedure.

Backward proton production and high-momentum components of nuclei

H. J. Weber and L. D. Miller

Phys. Rev. C 16, 726 (1977) - Published 1 August, 1977

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The production of energetic protons at 180° by the inclusive reaction $A (p, p^{'}) X$ is studied. A mechanism which involves $A - 1$ nucleon transfer and relates the inclusive cross section to the total cross section $σ_{T} (p, A - 1)$ and realistic nuclear single-particle momentum distributions gives a qualitative understanding of the data.

NUCLEAR REACTIONS Backward proton production $A (p, p^{'}) X$ , 600-800 MeV, nuclear single proton distributions (high $q$ ) calculated.

Energetic charged particle yields induced by pions on complex nuclei

H. E. Jackson, S. B. Kaufman, L. Meyer-Schützmeister, J. P. Schiffer, S. L. Tabor, S. E. Vigdor, J. N. Worthington, L. L. Rutledge, Jr., R. E. Segel, R. L. Burman, P. A. M. Gram, R. P. Redwine, and M. A. Yates

Phys. Rev. C 16, 730 (1977) - Published 1 August, 1977

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The spectra of protons ( $60 < E_{p} < 200$ MeV) and deuterons ( $80 MeV < E_{d}$ ) produced by 100- and 220-MeV $π^{+}$ and $π^{-}$ on Al, Ni, and Ta targets were measured. The shapes of proton spectra are similar for $π^{+}$ and $π^{-}$ , with absolute yields in ∼3:1 ratio; the yields vary as $\sim A^{\frac{2}{3}}$ . The exception is the forward-angle yield at 100 MeV where the proton spectra with $π^{+}$ are different in shape from $π^{-}$ , the yield ∼5 times as high, and the target dependence is $\sim A^{\frac{1}{3}}$ . This pattern is not readily understood at the present time.

NUCLEAR REACTIONS ${}^{27}{Al}$ , ${}^{62}{Ni}$ , ${}^{181}{Ta}$ , ( $π^{\pm}, p$ ), and ( $π^{\pm}, d$ ). $E_{π} = 100, 220$ MeV, $θ = 45, 94 °$ ; measured $\frac{d^{2} σ}{d Ω dE}$ for $50 < E_{p} < 200$ MeV and $80 < E_{d} < 200$ MeV.

$π^{-}$ -nucleus interactions for stopped and 45 MeV pions with ${}^{58, 60, 62}{Ni}$

Y. Cassagnou, H. E. Jackson, J. Julien, R. Legrain, L. Roussel, S. Barbarino, and A. Palmeri

Phys. Rev. C 16, 741 (1977) - Published 1 August, 1977

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The spectra of residual nuclei produced by the interaction of stopped and 45 MeV $π^{-}$ has been studied as a function of neutron excess in the nickel isotopes. The similarity of results for stopped pions and pions in flight indicates that absorption is the dominant mode of interaction. While the data show substantial departures from trends observed in measurements reported previously at higher energies, the same mechanism appears to explain the reaction in all cases.

NUCLEAR REACTIONS ${}^{58, 60, 62}{Ni}$ , $(π^{-}, ?) γ$ inclusive $γ$ ray spectra, $E_{π} = 0 and 45$ MeV. Production cross sections for residual nuclei, quasideuteron pion absorption model.

Unique first forbidden beta decay of ${}^{183}{Re}$ and ${}^{185}{Os}$

D. S. Brenner, M. Lindner, and R. A. Meyer

Phys. Rev. C 16, 747 (1977) - Published 1 August, 1977

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The decays of ${}^{183}{Re}$ and ${}^{185}{Os}$ were studied by $γ$ -ray spectroscopy using Ge(Li) detectors. The $log f_{1} t$ value for the 5/2 ${5 / 2}^{+}$ [402]→9/2 ${1 / 2}^{-}$ [510] transition between ${}^{183}{Re}$ and ${}^{183}W$ was 9.3, which contrasts to the previously reported value of 8.0. The 5/2 ${1 / 2}^{+}$ [402] $K - 2$ $γ$ -vibrational state of ${}^{185}{Re}$ was identified for the first time at 768.93 keV. This level is populated from the 1/2 ${1 / 2}^{-}$ [510] ground state of ${}^{185}{Os}$ with a $log f_{1} t$ value of 10.4.

RADIOACTIVITY ${}^{183}{Re}$ [from ${}^{182}W (α, 3 n)$ , $W (α, x n)$ (9.9-h, 14-h, EC) ${}^{183}{Re}$ ]; ${}^{185}{Os}$ [from $W (α, x n)$ ; measured $E_{γ}$ , $I_{γ}$ , $T_{\frac{1}{2}}$ , deduced $log ft$ , ${}^{183}W$ , ${}^{185}{Re}$ deduced levels, $J$ , $π$ . Ge(Li) detectors; enriched, natural targets.

Limit on Fierz interference in nuclear beta decay

Barry R. Holstein

Phys. Rev. C 16, 753 (1977) - Published 1 August, 1977

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Nuclear level density with realistic interactions

F. N. Choudhury and S. Das Gupta

Phys. Rev. C 16, 757 (1977) - Published 1 August, 1977

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A formalism is developed which can be used to calculate nuclear level densities with realistic interactions. The grand partition function is constructed and the level density is obtained by Laplace inversion. The formalism is a generalization of the technique used when the only residual interaction is the pairing force. It takes into account both Hartree-Fock and pairing-type effects. Illustrative examples are given.

NUCLEAR STRUCTURE Formulated method for calculating nuclear level density with realistic interactions.

Validity of the particle-vibration model

J. M. Greben

Phys. Rev. C 16, 767 (1977) - Published 1 August, 1977

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The validity of various approximations in the particle-vibration model has been studied for the particle-vibration multiplet in ${}^{209}{Bi}$ . It is shown that the Pauli exclusion principle is taken into account by this model. Since the diagonal particle-vibration coupling, which is neglected in the particle-vibration model, has a sizable effect on the energy splittings, we have studied this interaction in detail. We show that its multipole structure is rather complex, so that it cannot easily be represented by a phenomenological model. The validity of certain symmetry relations in the particle-vibration model has been investigated. This study indicates that the particle-vibration model overestimates the influence of multiphonon intermediate states. Other multiplets in the lead region are briefly discussed, as well.

NUCLEAR STRUCTURE Interactions between vibrational and fermion degrees of freedom. Approximations in the particle-vibration model. Septuplet in ${}^{209}{Bi}$ .

Nucleon-nucleon interaction in nuclear matter

Sadhan K. Adhikari, H. T. Coelho, F. A. Bezerra Coutinho, and Y. Nogami

Phys. Rev. C 16, 777 (1977) - Published 1 August, 1977

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The effective two-body $NN$ potential in nuclear matter due to the two-pion-exchange three-body force can be expressed such that it arises due to a change in the pion propagator pertaining to the one-pion-exchange potential. The pion propagator in nuclear matter is examined with the $NN$ correlation taken into account. It is found that the modified propagator can be approximated by ${[(1 - α) (q^{2} + {μ^{'}}^{2})]}^{- 1}$ where $μ^{'} = μ {(1 - α)}^{- \frac{1}{2}}$ , $μ$ is the pion mass, and $α$ is a positive constant which is roughly proportional to the nuclear matter density. For example, $α \approx 0.3$ for the normal density of nuclear matter. The modified one-pion-exchange potential in nuclear matter is then obtained by scaling the one-pion-exchange potential in vacuum. It is suggested that other parts of the $NN$ potential, e.g., the two-pion-exchange part, are also modified by the same mechanism, and hence the $NN$ interaction in nuclear matter could be strongly density dependent.

NUCLEAR STRUCTURE Pion propagator in nuclear matter, many-body forces.

Effective interactions: Qualitative discussion of Hartree-Fock effects

F. L. Goodin, P. J. Ellis, and P. R. Goode

Phys. Rev. C 16, 784 (1977) - Published 1 August, 1977

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We calculate the effective interaction for ${}^{18}O$ in a simulated Hartree-Fock basis by taking a fixed oscillator parameter of 1.7 fm for the $s$ and $p$ shells and a variable parameter $b_{u}$ for the $sd$ and $pf$ shells. A central interaction is used and diagrams of first, second, and third order in $V$ are calculated. The dominant effect is one of scaling with diagrams of second and third order all decreasing in the same exponential fashion as a function of $b_{u}$ . Comparing pure oscillator ( $b_{u} = 1.7$ fm) and simulated Hartree-Fock ( $b_{u} = 2.0$ fm) results, we find a reduction factor of roughly 0.7, ${0.7}^{2}$ , and ${0.7}^{3}$ for first, second, and third order, respectively. Diagrams containing a particle-particle ladder usually fall off somewhat less rapidly than the others. The implications of these model results are discussed.

NUCLEAR STRUCTURE Effective interaction theory; model simulation of a Hartree-Fock basis.

Effective charges and $E 2$ transitions in $1 f - 2 p$ shell nuclei

A. K. Dhar and K. H. Bhatt

Phys. Rev. C 16, 792 (1977) - Published 1 August, 1977

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The proton and neutron effective charges needed to reproduce the observed $E 2$ data on the transitions between the ground state bands of the isotopes of $Ti (A = 44 - 50)$ , $V (A = 47 - 51)$ , $Cr (A = 48 - 52)$ , and $Fe (A = 52, 54)$ are found to be $e_{p} = (1.33 \pm 0.09)$ e, $e_{n} = (0.64 \pm 0.10)$ e. These charges were obtained by a least-squares fit between the deformed configuration mixing shell model calculated and the observed $B (E 2)$ values for the transitions in these nuclei. These values support the charges $e_{p} = 1.25$ e, $e_{n} = 0.47$ e obtained recently by Kuo and Osnes in a microscopic calculation and the charges $e_{p} = 1.21$ e, $e_{n} = 0.79$ e obtained on the basis of macroscopic estimates of Bohr and Mottelson.

NUCLEAR STRUCTURE Semiempirical effective charges, $B (E 2)$ values for transitions in $Ti (A = 44 - 51)$ , $V (A = 47 - 49, 51)$ , $Cr (A = 48 - 50, 52)$ , and $Fe (A = 52, 54)$ nuclei calculated within deformed configuration mixed calculations based on projected Hartree-Fock theory within ${(fp)}^{n}$ space.

Mode coupling and Dyson's finite boson expansion in nuclei

P. Ring and P. Schuck

Phys. Rev. C 16, 801 (1977) - Published 1 August, 1977

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In recent papers we developed and applied a mode (weak) coupling method for nuclei which show weak anharmonicity. In this work we demonstrate that this approach is rigorously equivalent to Dyson's finite boson expansion which has been generalized for nuclei by Janssen et al. We discuss here in detail the advantages and drawbacks of Dyson's method as for instance the appearance and localization of spurious states due to a violation of the Pauli principle. We also give a very simple prescription for calculating matrix elements in Dyson's method.

NUCLEAR STRUCTURE Theory boson expansion method.

Sum rules and mean excitation energies for longitudinal isoscalar electroexcitation of nuclei

E. Lipparini, G. Orlandini, and R. Leonardi

Phys. Rev. C 16, 812 (1977) - Published 1 August, 1977

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A useful momentum dependent sum rule is discussed for the longitudinal isoscalar electroexcitation of nuclei; combining this sum rule with the Kao-Fallieros sum rule, we study the momentum dependence of the mean excitation energy of the electroexcitation operator. For low momentum transfer this operator reduces to the monopole operator. Detailed results are given for ${}^{16}O$ and ${}^{208}{Pb}$ .

NUCLEAR STRUCTURE Momentum dependence of longitudinal isoscalar electro-excitation energy studied with sum rules. RPA accuracy.

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Recent Issues

Back-angle anomalies in ${}^{6}{Li}$ scattering from ${}^{40}{Ca}$ and ${}^{44}{Ca}$

Comparison of light- and heavy-ion emission from the ${}^{12}C$ + ${}^{16}O$ system

Magnetic moment and lifetime of the first excited state of mirror nuclei ${}^{21}{Ne}$ and ${}^{21}{Na}$

Reactions of ${}^{237}{Np}$ with ${}^{4}{He}$ near the interaction barrier

Fission and neutron emission in the actinides at excitation energies of 10-35 MeV

Fission probability calculations for heavy-ion induced reactions

Kinetic-energy distributions in the reactor neutron fission of ${}^{232}U$ and thermal neutron fission of ${}^{241}{Pu}$ and ${}^{245}{Cm}$

Inverse scattering problem with isobars

Backward proton production and high-momentum components of nuclei

Energetic charged particle yields induced by pions on complex nuclei

$π^{-}$ -nucleus interactions for stopped and 45 MeV pions with ${}^{58, 60, 62}{Ni}$

Unique first forbidden beta decay of ${}^{183}{Re}$ and ${}^{185}{Os}$

Limit on Fierz interference in nuclear beta decay

Nuclear level density with realistic interactions

Validity of the particle-vibration model

Nucleon-nucleon interaction in nuclear matter

Effective interactions: Qualitative discussion of Hartree-Fock effects

Effective charges and $E 2$ transitions in $1 f - 2 p$ shell nuclei

Mode coupling and Dyson's finite boson expansion in nuclei

Sum rules and mean excitation energies for longitudinal isoscalar electroexcitation of nuclei

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