Recent Articles

Neutron-Induced Fission Cross Section of ${}^{252}{Cf}$

M. S. Moore, J. H. McNally, and R. D. Baybarz

Phys. Rev. C 4, 273 (1971) - Published 1 July, 1971

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The neutron-induced fission cross section of ${}^{252}{Cf}$ was measured from 20-eV to 5-MeV neutron energy, using neutrons from the Physics-8 nuclear explosion. Pronounced sub-barrier resonance fission is observed below a few keV neutron energy. The fission threshold is found to occur at ∼900 keV. Analysis of the data indicates that the fission barrier is quite transparent, giving an average fission width comparable to the value of 0.02-0.05 eV expected for the average radiative capture width in the resonance region.

Strength of First Excited $0^{+}$ State of the $U^{238} (p, t) U^{236}$ Reaction near 27 MeV

J. R. Comfort, J. R. Duray, and W. J. Braithwaite

Phys. Rev. C 4, 277 (1971) - Published 1 July, 1971

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The $U^{238} (p, t) U^{236}$ reaction was studied with 27.34-MeV protons, and the ratio of the yield of the first excited $0^{+}$ state to that of the ground state was found to be 0.14 ± 0.03. The excellent agreement with the value previously obtained with 17-MeV protons supports the view that such unusual strength reflects a new type of collective mode for this state.

Nondirect ${}^{26}{Mg}$ ( ${}^{4}{He}$ , ${}^{6}{He}$ ) ${}^{24}{Mg}$ Reaction at 35 MeV

R. J. Peterson, H. W. Baer, H. H. Chang, and B. W. Ridley

Phys. Rev. C 4, 278 (1971) - Published 1 July, 1971

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The differential cross sections for the two-neutron pickup reaction ${}^{26}{Mg}$ ( ${}^{4}{He}$ , ${}^{6}{He}$ ) ${}^{24}{Mg}$ have been found to exhibit a strong dependence on bombarding energy, evidence of some process other than a direct reaction. Angular distributions at a fixed energy for several low-lying states of ${}^{24}{Mg}$ are found to exhibit structure reminiscent of known direct reactions, and we conclude that this signature cannot be considered proof of a direct reaction.

Two- and Three-Nucleon Calculations with Rank-1 Tabakin Separable Interaction

R. W. Peacock and R. D. Purrington

Phys. Rev. C 4, 281 (1971) - Published 1 July, 1971

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Neutron-deuteron scattering phase shifts and angular distributions for laboratory energies of 2.45 and 3.27 MeV are calculated using the rank-1 separable potential of Tabakin in both the triplet and singlet states. It is found that the ${}^{2}S_{\frac{1}{2}}$ phase shift is in disagreement with phase-shift analyses of the data.

Complex Angular Momentum Methods in the Study of Nucleon-Nucleus Elastic Scattering

R. Shanta and R. K. Satpathy

Phys. Rev. C 4, 284 (1971) - Published 1 July, 1971

Investigation of the ${}^{207}{Pb} (α, d) {}^{209}{Bi}$ Reaction

M. B. Lewis, C. D. Goodman, and D. C. Hensley

Phys. Rev. C 4, 284 (1971) - Published 1 July, 1971

Probability of Production of Internal Bremsstrahlung Accompanying $β$ Decay from ${Tl}^{204}$ , ${Pm}^{147}$ , and ${Ca}^{45}$

B. Singh and Shetha S. Al-Dargazelli

Phys. Rev. C 4, 284 (1971) - Published 1 July, 1971

Approximation to the Relativistic Scattering Problem

Pao Lu and Edward M. Measure

Phys. Rev. C 4, 31 (1971) - Published 1 July, 1971

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We extend the calculation of the relativistic phase-shift problem, as given before, to second order in $ℏ$ by means of Miller and Good's modified WKB method. The scheme of Bertocchi, Fubini, and Furlan is used to avoid the divergences introduced in the second-order terms. The example indicates that the phase shifts are greatly improved at lower angular quantum numbers.

$n - {}^{4}{He}$ Elastic Scattering near 20 MeV

A. Niiler, M. Drosg, J. C. Hopkins, J. D. Seagrave, and E. C. Kerr

Phys. Rev. C 4, 36 (1971) - Published 1 July, 1971

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The differential cross sections for the elastic scattering of neutrons by ${}^{4}{He}$ have been measured at incident neutron energies of 17.6, 20.9, and 23.7 MeV for lab angles between 20 and 140°. The cross sections were measured relative to the ${}^{1}H (n, n) {}^{1}H$ cross sections by the neutron time-of-flight technique. The $0.75 - M {}^{4}{He}$ scattering sample was a liquid contained in a thin-walled cryostat. Corrections were made for multiple scattering and attenuation. Phase-shift analyses were performed using both differential-cross-section and polarization data. The present phase shifts are joined to the well-established low-energy phase shifts giving a smooth energy dependence.

Elastically Equivalent Potentials

J. E. Monahan, C. M. Shakin, and R. M. Thaler

Phys. Rev. C 4, 43 (1971) - Published 1 July, 1971

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We define a nondenumerably infinite class of two-body potentials that give $T$ matrix elements that are identical on the energy shell but are different off shell. The existence of this class is shown to be related to a nonuniqueness in the off-shell continuation of the Schrödinger equation. A relation for the difference between off-shell elements of $T$ matrices that are equal on shell is given in a form that is convenient for the systematic study of off-shell effects in systems of more than two nucleons. In particular, these relations allow one to investigate subclasses of elastically equivalent interaction potentials that satisfy restrictions such as finite range. The possibility that elastically equivalent interactions have different off-shell symmetry properties is discussed, and some observations concerning the use and interpretation of elastically equivalent potentials in many-body calculations are presented.

Accurate Measurements of the Nuclear Processes $T (p, p) T$ , $T (p, {}^{3}{He}) n$ , $T (p, d) D$ , and $T (\vec{p}, \hat{p}) T$ from 13 to 20 MeV

J. L. Detch, Jr., R. L. Hutson, Nelson Jarmie, and J. H. Jett

Phys. Rev. C 4, 52 (1971) - Published 1 July, 1971

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Differential cross sections have been measured with absolute accuracies of about 1.0% and relative accuracies of about 0.7% using a tritium gas target with thin foil windows and a silicon surface-barrier detector telescope in conjunction with an on-line computer for mass identification and data handling. The angular scattering distributions for $T (p, p) T$ , $T (p, d) D$ , and $T (p, {}^{3}{He}) n$ , and the proton asymmetries of $T (\vec{p}, \hat{p}) T$ were measured at a proton laboratory energy of 13.600 MeV. In addition, differential cross sections for $T (p, p) T$ were measured at energies of 16.230 and 19.480 MeV to provide supporting data for existing mass-4 studies at these energies.

Related data are compared and preliminary attempts to analyze the data with an energy-independent phase-shift-analysis program are discussed. Several sets of single-channel phase-shift solutions are given for maximum angular momentum $L$ values of 3. These solutions are not unique. Simultaneous two- and three-channel analyses have been inconclusive.

Polarization asymmetry measurements using the Los Alamos Scientific Laboratory Lamb-shift polarized ion source show a maximum analyzing power of about +0.70 at 13.600 MeV for $T (\vec{p}, \hat{p}) T$ . These values are related to existing analyzing power measurements of ${}^{3}{He} (\vec{p}, \hat{p}) {}^{3}{He}$ and $T (\vec{p}, \hat{p}) T$ near this energy.

$Λ$ Binding Energy for the $2 s - 1 d$ -Shell Hypernuclei. I. $18 <~ A <~ 21$

T. Y. Lee, S. T. Hsieh, W. W. Yeh, and C. T. Chen-Tsai

Phys. Rev. C 4, 64 (1971) - Published 1 July, 1971

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Polarization in $n - p$ Scattering from 11 to 29.6 MeV

G. S. Mutchler and J. E. Simmons

Phys. Rev. C 4, 67 (1971) - Published 1 July, 1971

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Measurements of neutron-proton polarizations at 90° c.m. have been made at 11.0, 16.8, 23.1, and 29.6 MeV. The results are: 0.0130 ± 0.0049, 0.0280 ± 0.0060, 0.0502 ± 0.0040, and 0.0824 ± 0.0066, respectively. The $T (d, n) {}^{4}{He}$ and $D (t, n) {}^{4}{He}$ reactions were used as sources of monoenergetic polarized neutrons. At 23.1 MeV the polarization was also measured at 70° c.m., and at 29.6 MeV additional measurements were made at 60 and 120° c.m. The 90° data are related to the $T = 1$ spin-orbit $P$ -wave splitting, $Δ_{LS}$ . Comparisons were made with current phase-shift analyses, with the result that near 23 and 30 MeV these data give values of $Δ_{LS}$ in accord with the analyses. Near 10 MeV the theoretical situation is less certain and the data place limits on the value of $Δ_{LS}$ .

Multiple-Scattering Expansions for Moderate-Energy Particle-Deuteron Scattering

K. L. Kowalski and S. C. Pieper

Phys. Rev. C 4, 74 (1971) - Published 1 July, 1971

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A multiple-scattering expansion based on a fixed-scatterer approximation is conjectured to be more appropriate for discussing the small-angle elastic scattering of particles from deuterium than the expansion derived from the Faddeev equations. Some computations carried out for nucleon-deuteron scattering in the energy range 10-100 MeV seem to lend support to this conjecture.

Brueckner-Hartree-Fock Calculations of Spherical Nuclei in a Harmonic-Oscillator Basis. III. Renormalized Calculations Using the Reid Potential

K. T. R. Davies and R. J. McCarthy

Phys. Rev. C 4, 81 (1971) - Published 1 July, 1971

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A $G$ matrix derived from the Reid soft-core potential is used in a series of Brueckner-Hartree-Fock calculations of spherical nuclei. The $G$ matrix is calculated using an intermediate-state spectrum and Pauli operator appropriate to pure oscillator orbitals, with options to shift the entire spectrum or the low-lying levels from unperturbed oscillator energies. The Pauli operator takes into account the filling of different neutron and proton subshells in $N \neq Z$ nuclei. Self-consistent occupation probabilities are included in the calculations and results are presented for ${}^{16}O$ , ${}^{40}{Ca}$ , ${}^{48}{Ca}$ , and ${}^{208}{Pb}$ . Various systematics and convergences are studied. Good results can be obtained for the binding energies, but the experimental binding energy and charge radius cannot be fitted simultaneously. It is shown that renormalization with occupation probabilities is crucial for calculating a reasonable single-particle spectrum. The difficulty of comparing single-particle energies with experiment is discussed with particular emphasis on heavy and superheavy nuclei. The nuclei ${}^{298}114$ and ${}^{310}126$ are calculated for a simple force.

Cross-Section Measurements for the Transfer Reactions ( ${}^{14}N$ , ${}^{13}N$ ) and ( ${}^{19}F$ , ${}^{18}F$ ) Induced on ${}^{19}F$ , ${}^{23}{Na}$ , and ${}^{51}V$

R. M. Gaedke, K. S. Toth, and I. R. Williams

Phys. Rev. C 4, 98 (1971) - Published 1 July, 1971

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Thick targets of ${}^{19}F$ , ${}^{23}{Na}$ , and ${}^{51}V$ were bombarded with ${}^{14}N$ and ${}^{19}F$ ions accelerated in the Oak Ridge tandem Van de Graaff accelerator. Cross sections were measured for the neutron transfer reactions ${}^{19}F$ ( ${}^{14}N$ , ${}^{15}N$ ) ${}^{18}F$ , ${}^{19}F$ ( ${}^{19}F$ , ${}^{18}F$ ) ${}^{20}F$ , ${}^{23}{Na}$ ( ${}^{19}F$ , ${}^{18}F$ ) ${}^{24}{Na}$ , ${}^{51}V$ ( ${}^{14}N$ , ${}^{13}N$ ) ${}^{52}V$ , and ${}^{51}V$ ( ${}^{19}F$ , ${}^{18}F$ ) ${}^{52}V$ at energies close to the Coulomb barriers for the various target and projectile combinations. The data were analyzed by the use of the tunneling theory of Breit et al. The theory was found to account for the shapes of the excitation functions of the first three reactions listed above. The excitation functions for the two reactions with ${}^{51}V$ as the target nucleus were found to have slopes that were steeper than that predicted by the tunneling theory. This is thought to be an indication that even at energies below the Coulomb barrier, excited states in ${}^{52}V$ are populated in the transfer process. By assuming that the neutron reduced width in ${}^{52}V$ is the same in both the ${}^{19}F$ - and ${}^{14}N$ -induced reactions, a reduced-width ratio was extracted for the transferred neutron in ${}^{19}F$ to that in ${}^{14}N$ . The ratio was found to be ∼2.0 as compared with values of ∼3.7 extracted earlier from low-energy cross-section data for ( ${}^{19}F$ , ${}^{18}F$ ) and ( ${}^{14}N$ , ${}^{13}N$ ) reactions on targets of ${}^{10}B$ and ${}^{14}N$ . If the ±30% error limits on the experimental cross sections are taken into account, the value of 2 is not in disagreement with the earlier determined ratios of 3.7. We feel, however, that the difference arises because transfers to the ground states in ${}^{11}B$ and ${}^{15}N$ are predominant at low bombarding energies. Since this is apparently not so for the reactions with ${}^{51}V$ (see above), the ${}^{19}F$ reaction may populate different states in ${}^{52}V$ than the ${}^{14}N$ reaction would populate; the reduced-width ratio would then not be the same as that extracted from the data with ${}^{10}B$ and ${}^{14}N$ targets.

${}^{6}{Li} (α, 2 α)$ Reaction as a Test of the Existence of $α$ Particles in ${}^{6}{Li}$

G. Deconninck, A. Giorni, J. P. Longequeue, J. P. Maillard, and Tsan Ung Chan

Phys. Rev. C 3, 2085 (1971) - Published 1 June, 1971

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The presence of a strong discontinuity in the free $α - α$ scattering amplitude at 40 MeV is used as a probe for the identification of $α$ clusters in nuclei. The ${}^{6}{Li} (α, 2 α)$ reaction is investigated at 37.5 and 43.5 MeV with the deuteron as spectator in order to produce quasifree scattering conditions. The distributions measured at these two energies are found to be very different in magnitude as well as in structure, and this phenomenon is attributed to the presence of $α - α$ scattering in the $α - {}^{6}{Li}$ collision. Calculations based on the plane-wave impulse approximation are unable to reproduce the distributions even qualitatively. A calculation based on the graph formalism which takes into account the exact phase-shift amplitude of the free $α - α$ collision fits the two distributions with the same set of parameters. One may conclude that these observations are in favor of the existence of $α$ particles inside the ${}^{6}{Li}$ nucleus.

Effective $s$ -Wave Interaction in Finite Nuclei

R. Muthukrishnan

Phys. Rev. C 3, 2091 (1971) - Published 1 June, 1971

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It is shown that a simple $s$ -wave separable interaction whose parameters are determined by a fit to the binding energy and density of nuclear matter, when modified by making the strength a smooth function of the mass number $A$ (such that the strength approaches that for nuclear matter as $A \to \infty$ ), gives the binding energy and radii of spherical nuclei throughout the Periodic Table in excellent agreement with experimental values. This behavior of the strength as a function of $A$ is discussed in the light of the results of calculations which use realistic interactions.

Probable Significance of Excitation Quantum Numbers in Nuclei

A. K. Dutta

Phys. Rev. C 3, 2095 (1971) - Published 1 June, 1971

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It has been found previously that analytic expressions for binding energies of nuclei in the isobaric form and for their excitation energies together with their superposed irregular deviations determine the binding and excitation energies of nuclei. The irregular deviations of the excited-state energies from the associated analytic expression for a particular ( $A, Z$ ) combination are determined by the corresponding irregular deviations of binding energy from its associated analytic expression. These deviations of binding energy are expected to be dependent on other irregular physical characteristics of nuclei and control, through their variations, the irregular deviations of excitation energies from the analytic part. The analytic part of the excitation energies for all nuclei consists of factors of which the first part is a function of $A$ and the second part is dependent on integral quantum numbers $n_{i}^{*}$ for different stages of excitations, with associated constants for all the even- or for the odd-nucleon numbers. The quantum numbers for nuclear excitation are thus independent of the characteristics of motion or of configurational changes and must therefore depend on some other purely nuclear characteristic of a general nature.

From a study of the method of evaluating excitation energies of nuclei by the $β$ -decay procedure and also from the study of nuclear reactions in small nuclei, it is considered that the mechanism causing excitations and that for isobaric changes in the ground state are very much alike. To conform to this allied character the analytic expression measuring isobaric energy change is brought into a form similar to the expression for excitation-energy change by replacing the parabolic factor ${(Z^{0} - Z)}^{2}$ for isobaric change in energy by the exponential factor [ $α^{+} n^{+} - 1$ ], where $n^{+} = | Z^{0} - Z |$ measures the number of replacements of protons by neutrons or vice versa externally. The values obtained by the exponential and the parabolic forms are close to each other in the effective region of isobaric parabolas when $σ^{+} = 0.78$ . Comparing the expressions for energy change due to excitation and that due to isobaric change, it is considered that the excitation quantum numbers $n_{i}^{*}$ measure the number of replacements internally of neutrons by protons or vice versa at successively higher levels.

Analyses of Elastic Proton-Alpha Scattering

Richard A. Arndt, L. David Roper, and Robert L. Shotwell

Phys. Rev. C 3, 2100 (1971) - Published 1 June, 1971

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Starting from reported single-energy analyses of $p - α$ elastic scattering we obtain an energy-dependent solution to $p - α$ scattering between 0 and 23 MeV. We also did single-energy analyses at energies where both differential-cross-section and polarization data are available starting from the energy-dependent solution. The single-energy results are rather erratie, but tend to lie near the energy-dependent result.

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Neutron-Induced Fission Cross Section of ${}^{252}{Cf}$

Strength of First Excited $0^{+}$ State of the $U^{238} (p, t) U^{236}$ Reaction near 27 MeV

Nondirect ${}^{26}{Mg}$ ( ${}^{4}{He}$ , ${}^{6}{He}$ ) ${}^{24}{Mg}$ Reaction at 35 MeV

Two- and Three-Nucleon Calculations with Rank-1 Tabakin Separable Interaction

Complex Angular Momentum Methods in the Study of Nucleon-Nucleus Elastic Scattering

Investigation of the ${}^{207}{Pb} (α, d) {}^{209}{Bi}$ Reaction

Probability of Production of Internal Bremsstrahlung Accompanying $β$ Decay from ${Tl}^{204}$ , ${Pm}^{147}$ , and ${Ca}^{45}$

Approximation to the Relativistic Scattering Problem

$n - {}^{4}{He}$ Elastic Scattering near 20 MeV

Elastically Equivalent Potentials

Accurate Measurements of the Nuclear Processes $T (p, p) T$ , $T (p, {}^{3}{He}) n$ , $T (p, d) D$ , and $T (\vec{p}, \hat{p}) T$ from 13 to 20 MeV

$Λ$ Binding Energy for the $2 s - 1 d$ -Shell Hypernuclei. I. $18 <~ A <~ 21$

Polarization in $n - p$ Scattering from 11 to 29.6 MeV

Multiple-Scattering Expansions for Moderate-Energy Particle-Deuteron Scattering

Brueckner-Hartree-Fock Calculations of Spherical Nuclei in a Harmonic-Oscillator Basis. III. Renormalized Calculations Using the Reid Potential

Cross-Section Measurements for the Transfer Reactions ( ${}^{14}N$ , ${}^{13}N$ ) and ( ${}^{19}F$ , ${}^{18}F$ ) Induced on ${}^{19}F$ , ${}^{23}{Na}$ , and ${}^{51}V$

${}^{6}{Li} (α, 2 α)$ Reaction as a Test of the Existence of $α$ Particles in ${}^{6}{Li}$

Effective $s$ -Wave Interaction in Finite Nuclei

Probable Significance of Excitation Quantum Numbers in Nuclei

Analyses of Elastic Proton-Alpha Scattering

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