Recent Articles

Charge Asymmetry Effects and the Trinucleon Binding-Energy Difference

B. F. Gibson and G. J. Stephenson, Jr.

Phys. Rev. C 8, 1222 (1973) - Published 1 October, 1973

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We demonstrate, using a separable-potential model, that the discrepancy between the observed ${}^{3}H$ - ${}^{3}{He}$ binding-energy difference and the calculated Coulomb energy does not necessarily imply that $| a_{n n} | > | a_{p p} |$ . This possibility arises from the relative insensitivity of the trinucleon binding energy to the scattering length as compared to the sensitivity to the effective range.

${}^{6}{Li} ({}^{3}{He}, t)$ Reaction and the Solar Neutrino Puzzle

M. L. Halbert, D. C. Hensley, and H. G. Bingham

Phys. Rev. C 8, 1226 (1973) - Published 1 October, 1973

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A search for a ${}^{3}{He}$ + ${}^{3}{He}$ resonance just above threshold was made by means of the reaction ${}^{6}{Li} ({}^{3}{He}, t) {}^{6}{Be}^{*}$ with 46.3-MeV ${}^{3}{He}$ . No resonance was found; the c.m. cross section is ≤1.6 μb/sr at 8.4° c.m. This corresponds to an upper limit on the spectroscopic factor for ${}^{6}{Be}^{*} \to {}^{3}{He} + {}^{3}{He}$ of 0.0003 to 0.001, depending on the parameters adopted for a distorted-wave Born-approximation calculation. The maximum possible effect of such a resonance on the production of high-energy solar neutrinos is too small to explain the discrepancy between solar-model predictions and the experimental results of Davis et al.

[NUCLEAR REACTIONS: ${}^{6}{Li} ({}^{3}{He}, t)$ , $E = 46.3$ MeV; measured $σ (E_{t}, θ = 5^{\circ})$ . Deduced: no ${}^{3}{He}$ - ${}^{3}{He}$ resonance in ${}^{6}{Be}$ .]

Isospin-Forbidden and - Allowed ${}^{16}O (d, α) {}^{14}N$ Reactions

P. L. Jolivette

Phys. Rev. C 8, 1230 (1973) - Published 1 October, 1973

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Cross sections are reported for the ${}^{16}O (d, α) {}^{14}N$ transitions to the ground and first excited state for $2 MeV \leq E_{d} \leq 14 MeV$ and 8-18 angles. An $S$ -matrix analysis of the isospin-forbidden reaction to the ${}^{14}N$ (2.31-MeV) $T = 1$ state yields level parameters, spins, and parities for a large number of ${}^{18}F$ intermediate states. Several of these are analogs of $T = 1$ levels in ${}^{18}O$ . The mechanisms for the isospin-forbidden reaction is entirely compound nuclear and for the isospin-allowed transition is predominantly so. The isospin impurity, averaged over 1-MeV intervals, is 3-10% for $10 \leq E_{x} ({}^{18}F) \leq 20$ MeV. Analysis by peak counting indicates that $\frac{Γ_{J}}{D_{J}} \sim 1$ at $E_{x} = 14$ MeV and that the average coherence width increases from ∼ 100 keV at $E_{x} = 14$ MeV to ∼ 500 keV at $E_{x} = 20$ MeV.

Neutron Polarization from ${}^{2}H (p, \vec{n})$ and ${}^{1}H (d, \vec{n})$

F. N. Rad, L. C. Northcliffe, D. P. Saylor, J. G. Rogers, and R. G. Graves

Phys. Rev. C 8, 1248 (1973) - Published 1 October, 1973

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Measurements of the neutron polarization in the $p - d$ breakup reaction are reported. The polarization of breakup neutrons from ${}^{2}H (p, \vec{n})$ has been measured at $E_{p} = 21.4$ MeV, $θ_{lab} = 18^{\circ}$ , as a function of neutron energy with an accuracy of approximately ±0.01. The measurement is consistent with zero from 8 to 13 MeV, but shows a small but significant positive polarization from 14 to 18 MeV. A similar measurement of the breakup neutrons from the ${}^{1}H (d, \vec{n}) 2 p$ reaction at the same center-of-mass momentum ( $E_{d} = 42.8$ MeV), also at $θ_{lab} = 18^{\circ}$ , shows nonzero polarization over the neutron energy region 8 to 25 MeV, reaching a maximum of about -0.05±0.01. In both cases, the polarization of the breakup neutrons is opposite in sign to that expected if the dominant process is simple quasifree scattering.

Generalization of the Jost Function and Its Application to Off-Shell Scattering

Michael G. Fuda and James S. Whiting

Phys. Rev. C 8, 1255 (1973) - Published 1 October, 1973

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An off-shell generalization of the Jost function is developed within the framework of the differential-equation approach to the off-shell $T$ matrix. Irregular solutions of the inhomogeneous Schrödinger-like equation that occurs in this approach are introduced, and their behavior at the origin is used to define an off-shell Jost function. The half-off-shell $T$ matrix is expressed directly in terms of the off-shell Jost function. It is shown how the fully off-shell $T$ matrix for a particular partial wave can be expressed simply in terms of a single integral involving the irregular solution for that partial wave. An integral equation for the irregular solution is developed, and used to derive an integral representation for the off-shell Jost function. Iteration of the integral equation leads to a series of successive approximations to the $T$ matrix. The formalism is applied to several examples, including a boundary-condition model.

Analyzing Power for $d - {}^{4}{He}$ Elastic Scattering at 12.0, 14.0, and 17.0 MeV

Gerald G. Ohlsen, P. A. Lovoi, G. C. Salzman, U. Meyer-Berkhout, C. K. Mitchell, and W. Grüebler

Phys. Rev. C 8, 1262 (1973) - Published 1 October, 1973

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Angular distributions of the analyzing tensors for $d - {}^{4}{He}$ elastic scattering in the angular range 30-145° (c.m.) and at 12, 14, and 17 MeV are presented. An over-all absolute precision of about ±0.01 is obtained. In addition to the complete angular distributions, data were taken in a fine mesh near 12 MeV, 37° (lab), where the analyzing tensor $A_{yy}$ apparently approaches unity. The manner in which it can be decided whether or not $A_{yy}$ goes to exactly unity is discussed. If this is found to be the case, a valuable absolute polarization standard will be available.

Correlation Effects in Nuclear Densities

M. R. Strayer, W. H. Bassichis, and A. K. Kerman

Phys. Rev. C 8, 1269 (1973) - Published 1 October, 1973

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Corrections to nuclear densities arising from static short-range correlations are evaluated for the nuclei ${}^{16}O$ , ${}^{40}{Ca}$ , and ${}^{56}{Ni}$ . The corrections are calculated using Rayleigh-Schrödinger perturbation theory in a basis obtained using Hartree-Fock. All corrections which are second order in the interaction are treated. The effects of necessary truncations are studied and are shown to render the results uncertain by about 20%. The net change in the density is a radial function which is less than 6% of the Hartree-Fock density and which oscillates in such a way that its effect on the rms radius is negligible. It is pointed out that in Brueckner-Hartree-Fock calculations a certain lack of cancellation might result in an excessively large change in the density and radius.

[NUCLEAR STRUCTURE calculated $ρ$ and rms radius. Hartree-Fock plus second-order corrections.]

Separable-Interaction Model for Deuteron Breakup

Jon M. Wallace

Phys. Rev. C 8, 1275 (1973) - Published 1 October, 1973

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This paper is the second in a planned series of papers in which is developed an exactly soluble three-nucleon model for describing $Nd$ scattering processes at energies above 30 MeV. The model described here is a small refinement of the one previously described. It is obtained from the low-energy three-body model of Aaron, Amado, and Yam by a simple modification of the $S$ -wave separable two-body amplitudes to fit two-nucleon elastic scattering data at higher energies. By comparison of the calculated differential cross sections with experiment at proton projectile energies of 46, 65, 85, 100, and 156 MeV, the model is shown to provide a reasonable description of the ${}^{2}H (p, 2 p)$ and ${}^{2}H (p, p n)$ reactions throughout this energy range. Some quantitative justification for the two-nucleon amplitudes employed supplants the hand-waving arguments of the first paper.

Beta Decay of ${}^{17}N$

A. R. Poletti and J. G. Pronko

Phys. Rev. C 8, 1285 (1973) - Published 1 October, 1973

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The delayed-neutron and $γ$ -ray spectra following the $β$ decay of ${}^{17}N$ have been investigated using the $β - n$ time-of-flight method, $β - γ$ coincidences, and neutron spectrometry. The following branchings have been determined for the $γ$ decay of ${}^{17}N$ to established energy levels in ${}^{17}O$ : decay to ground state (1.7±0.5%), 0.87 MeV (2.9±0.5%), 3.06 MeV (0.54±0.08%), 4.55 MeV (37.9±1.8%), 5.377 MeV (51.1±1.5%), and 5.935 MeV (5.8±0.6%). The latter three states are particle unstable and decay by the emission of neutrons to the ground state of ${}^{16}O$ . The energies of these neutron groups as determined by us were, respectively, 0.385±0.004, 1.163±0.014, and 1.675±0.024 MeV. The results are discussed and compared to theoretical calculations. The measured $β$ -decay strengths are compared to the strengths of corresponding transitions in the $β$ decay of the mirror nucleus ${}^{17}{Ne}$ .

$T$ -Matrix Perturbation Theory for the Three-Nucleon System with the Reid Potential

I. R. Afnan and J. M. Read

Phys. Rev. C 8, 1294 (1973) - Published 1 October, 1973

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The binding energy of ${}^{3}H$ for the Reid soft-core ${}^{1}S_{0}$ and ${}^{3}S_{1} - {}^{3}D_{1}$ potentials was determined, using $T$ -matrix perturbation theory, to be 7.02 MeV. The one-term separable approximation to the Reid potential, constructed using the deuteron wave function in the ${}^{3}S_{1} - {}^{3}D_{1}$ channel and the form factor associated with the antibound state in the ${}^{1}S_{0}$ channel, gave a binding energy of 7.15 MeV. This is close enough to the exact answer to be very useful in realistic three-nucleon calculations. It also demonstrates the important contribution that the two-body bound state wave functions make to the triton binding energy.

Mesonic Second-Class Currents in Nuclear $β$ Decay

B. Eman, B. Guberina, and D. Tadić

Phys. Rev. C 8, 1301 (1973) - Published 1 October, 1973

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Mesonic second-class currents have been studied in semileptonic $Δ S = 0$ transitions. The closed-loop diagram is finite for the $π ω$ current, and its energy-dependent lepton part is dominant over the contributions from the two-body exchange diagram. The two-body exchange diagram has energy-dependent and energy-independent lepton parts, which are of comparable magnitude for the $A = 12$ triplet. A general form of the mesonic current has also been considered. A general theory of second-class effects, including both mesonic currents and the induced-tensor term for $ft$ values and $\frac{K}{β^{+}}$ ratios, has been discussed.

Internal Excitation and Ionization Accompanying $K$ Capture

Takeshi Mukoyama, Yasuhito Isozumi, Tetsuo Kitahara, and Sakae Shimizu

Phys. Rev. C 8, 1308 (1973) - Published 1 October, 1973

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The internal excitation and ionization probabilities during $K$ -electron capture have been treated relativistically by the use of hydrogenic wave functions. Relativistic and nonrelativistic calculations for the double $K$ -hole production probability, the total internal ionization probability, and the energy spectrum of the ejected electrons are presented. The present calculations show that the relativistic effects cause a substantial reduction in the probabilities. The calculated probabilities of the double $K$ -hole production and the total internal ionization have been compared with the experimental values, and there has been fairly good agreement between the calculated and the recently measured values. The spectral shape of the ejected electrons calculated from the present relativistic theory is similar to that obtained from the previous nonrelativistic and relativistic theories. The theoretical curves are in good agreement with the experimental results in the high-energy region. The discrepancies between the theory and the various experiments are discussed and further work is suggested.

Directional Correlations of Gamma Rays in ${}^{79}{Br}$

M. A. Ludington, P. L. Gardulski, and M. L. Wiedenbeck

Phys. Rev. C 8, 1319 (1973) - Published 1 October, 1973

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The $γ$ radiation following the decay of ${}^{79}{Kr}$ to levels in ${}^{79}{Br}$ has been studied with Ge(Li) detectors. 40 transitions were observed, including 4 which were previously unreported. $γ - γ$ directional-correlation measurements have been made using two Ge(Li) detectors. The $\frac{E 2}{M 1}$ amplitude mixing ratios for several transitions in ${}^{79}{Br}$ have been determined from these directional-correlation measurements. The results of these measurements together with conversion coefficients and $log ft$ values have made it possible to assign spins and parities to some of the excited levels.

Accurate Masses and $β$ -Decay Schemes for ${}^{34}P$ and ${}^{33}{Si}$

D. R. Goosman, C. N. Davids, and D. E. Alburger

Phys. Rev. C 8, 1324 (1973) - Published 1 October, 1973

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By using delayed $β - γ$ coincidence techniques, the mass excesses of ${}^{34}P$ and ${}^{33}{Si}$ have been measured to be -24 546 ± 45 and -20 569 ± 50 keV, respectively, representing improvements in precision of a factor of 2 for ${}^{34}P$ and a factor of 4 for ${}^{33}{Si}$ over previous measurements. The first measurements of the high-energy $γ$ rays from ${}^{34}P$ decay with a Ge(Li) detector are presented, revealing three new $β$ branches. $γ$ -ray energies (in keV) and relative intensities for the ${}^{34}S$ daughter transitions are 1787 ± 1 (0.30 ± 0.10), 1947.1 ± 1.5 (0.28 ± 0.10), 1987.2 ± 1.0 (1.0 ± 0.2), 2127.4 (100.0 ± 0.3), 4073.4 ± 1.5 (0.46 ± 0.06), and 4114.0 ± 1.5 (1.2 ± 0.2). The ${}^{34}S$ excitation energies and relative $β$ branches are 2127.4 (100 ± 0.3), 3303.7 (<0.26), 3914.2 (0.30 ± 0.10), 4073.0 (0.76 ± 0.12), and 4114.5 (2.2 ± 0.3). For the decay of ${}^{33}{Si}$ , energies and relative intensities of $γ$ rays were measured to be 415.8 ± 0.6 (6.7 ± 0.6), 1431.4 (13.1 ± 1.0), 1847.5 (100 ± 1), and 2537.5 (9.3 ± 0.8), representing excitation energies and relative $β$ -ray intensities to the ${}^{33}P$ daughter states of 1431.4 ( ${5.1}_{- 2.4}^{+ 1.0}$ ), 1847.5 ( $100_{- 2.8}^{+ 1.0}$ ), and 2537.6 (10.5 ± 1.0). The half-lives of ${}^{34}P$ and ${}^{33}{Si}$ were determined by multiscaling $γ$ -ray yields to be 12.45 ± 0.10 and 6.11 ± 0.21 sec, respectively. Combined with an earlier result, a half-life of 6.18 ± 0.18 sec is adopted for ${}^{33}{Si}$ . The transverse mass relationship of Garvey, using the present measurements for ${}^{34}P$ and ${}^{33}{Si}$ , predicts a mass excess of -20 251 ± 90 keV for the $T_{z} = 3$ nuclide ${}^{34}{Si}$ .

Mass and $β$ Decay of the New Isotope ${}^{29}{Mg}$ : Systematics of Masses of $T_{z} = \frac{5}{2}$ Nuclides in the $2 s - 1 d$ Shell

D. R. Goosman, C. N. Davids, and D. E. Alburger

Phys. Rev. C 8, 1331 (1973) - Published 1 October, 1973

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Measurements of the mass, half-life, and $β$ decay of the new isotope ${}^{29}{Mg}$ are reported. Produced by the ${}^{18}O ({}^{13}C, 2 p) {}^{29}{Mg}$ reaction, this activity was periodically transferred to remotely located Ge(Li) and NE 102 detectors. $γ$ -ray energies (in keV) and relative intensities for the ${}^{29}{Al}$ daughter transitions are 960.3 ± 0.4 (52 ± 18), 1397.7 ± 0.4 ( $64_{- 20}^{+ 30}$ ), 1430 ± 1.5 (34 ± 17), 1753.8 ± 0.4 (22 ± 5), and 2223.7 ± 0.4 (100 ± 6). The ${}^{29}{Al}$ excitation energies (in keV) and relative $β$ branching intensities are 1397.7 ± 0.4 ( $64_{- 28}^{+ 35}$ ), 1753.8 ± 0.4 (<10), 2223.8 ± 0.4 (55 ± 22), and 3184.0 ± 0.6 (100 ± 35). Upper limits on other possible transitions are given. ${}^{29}{Mg}$ decays with a half-life of 1.20 ± 0.13 sec, measured by the decay of the prominent 2224-keV $γ$ ray. The decay of ${}^{29}{Mg}$ is discussed in terms of the Nilsson model. By measuring the spectrum of pulses in the NE 102 detector coincident with 2224-keV $γ$ rays, the mass excess for ${}^{29}{Mg}$ has been determined to be -10 590 ± 400 keV, disagreeing by 1.7 ± 0.5 MeV from a previous report. The present mass for ${}^{29}{Mg}$ is combined with all other information concerning masses of $T_{z} = \frac{5}{2}$ nuclides in the $2 s - 1 d$ shell, and the results are compared with predictions based upon measured masses closer to stability using the transverse relationship of Garvey. When the differences between the measured and predicted values are plotted against atomic weight, systematic effects are evident.

Neutron Polarization in Isospin-Forbidden ( $p, n$ ) Reactions

J. E. Monahan and A. J. Elwyn

Phys. Rev. C 8, 1339 (1973) - Published 1 October, 1973

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It is shown that the angular distributions of the yield and of the polarization of neutrons in isospin-forbidden ( $p, n$ ) reactions can provide a test of the statistical assumptions that are usually made in the analysis of isobaric-analog-resonance reactions. Also, under certain specified conditions, such measurements can detect any significant neutron width acquired by the analog state via Coulomb mixing with the $T_{<}$ background states. Recent measurements of the yield and polarization for the ${}^{51}V (p, n) {}^{51}{Cr}$ reaction in the neighborhood of the analog resonance observed at a proton energy of ∼2.335 MeV are discussed in terms of the present results. However, this particular example provides no unambiguous information about the mechanism that causes a breakdown of the statistical model or about a possible enhancement of the neutron width in the vicinity of the analog.

Spin and Parity of ${}^{20}F$ Levels from Gamma-Ray Linear-Polarization Measurements

D. S. Longo, J. C. Lawson, L. A. Alexander, B. P. Hichwa, and P. R. Chagnon

Phys. Rev. C 8, 1347 (1973) - Published 1 October, 1973

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The status of experimental quantum number assignments to low-lying levels of ${}^{20}F$ is reviewed. The use of a Compton-scattering polarimeter of limited resolution but good efficiency, in coincidence with an annular particle detector and perpendicular to the reaction symmetry axis, is described. Measurements of ${}^{20}{F^{*} deexcitation}$ $γ$ -ray polarization have been carried out following the ${}^{18}O ({}^{3}{He}, p)$ reaction at 3.8 MeV and 0°. In conjunction with past experiments, the following assignments are inferred: 656 keV, $3^{+}$ ; 823 keV, $4^{+}$ ; 984 keV, $1^{-}$ ; 1309 keV, $2^{-}$ ; 1824 keV, $5^{+}$ ; and 1843 keV, ( $2^{-}$ ). The relation of the experimental level structure to the rotational band grouping and to the $pds$ shell-model calculation of McGrory and and Wildenthal is illustrated.

${}^{86, 88}{Sr} (d, {}^{3}{He}) {}^{85, 87}{Rb}$ Reactions and a Possible $Z = 38$ Magic Number

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

Phys. Rev. C 8, 1354 (1973) - Published 1 October, 1973

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The ${}^{86, 88}{Sr} (d, {}^{3}{He}) {}^{85, 87}{Rb}$ reactions were studied at a bombarding energy of 28 MeV and angular distributions were obtained for all observed states. Spectroscopic factors were extracted from distorted-wave Born-approximation calculations of the cross sections. These spectroscopic factors, and those from the ${}^{86, 88}{Sr} ({}^{3}{He}, d) {}^{87, 89}Y$ reactions, were renormalized to satisfy sum-rule constraints. Some configuration mixing in the ground state of ${}^{88}{Sr}$ is inferred. The two $g_{\frac{9}{2}}$ neutron holes in ${}^{86}{Sr}$ produce very sizable rearrangements of the proton orbital populations in ${}^{86}{Sr}$ .

Compound-Nucleus Contribution for ( $p, α$ ) Reaction from Sn and Cd Isotopes

K. C. Chan, G. R. Rao, B. L. Cohen, J. H. Degnan, and L. Shabason

Phys. Rev. C 8, 1363 (1973) - Published 1 October, 1973

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A clean separation of compound-nucleus and direct-reaction processes in ( $p, α$ ) reaction was made for 12- and 17-MeV protons bombarding on Cd and Sn isotopes. Results indicated the compound-nucleus contributions for ${}^{112}{Sn}$ give isotropic angular distribution for the $α$ particles. Shapes of the energy spectra of emitted $α$ particles were in good agreement with statistical theory calculation, but absolute cross sections were larger than predicted by a factor of 2 to 7.

Radiative Capture of $S$ Electrons in the Decay of ${}^{51}{Cr}$

Manfred Mutterer

Phys. Rev. C 8, 1370 (1973) - Published 1 October, 1973

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The high-energy portion of the spectrum of internal-bremsstrahlung photons accompanying the allowed electron-capture transition from ${}^{51}{Cr}$ to the ground state of ${}^{51}V$ has been measured with a Ge(Li) $γ$ -ray spectrometer supplied with a pileup rejector. The most important correction for the residual pileup spectrum caused by the 320.1-keV nuclear $γ$ rays from the deexcitation of the first excited state in ${}^{51}V$ was performed by extrapolation from a set of measurements with sources of different activities. The pulse-height spectrum of internalbremsstrahlung photons was corrected for detector response. For energies higher than 348.1 keV the number of bremsstrahlung photons emitted per ground-state electron-capture (EC) decay of ${}^{51}{Cr}$ was determined to be (9.56 ± 0.60) × $10^{- 5}$ . Corresponding theoretical values are 9.49 × $10^{- 5}$ predicted by the theory of Martin and Glauber, and 9.47 × $10^{- 5}$ deduced from recent calculations of Intemann. The present result confirms the predictions of theory for radiative capture of $1 s + 2 s$ orbital electrons, in contradiction to recent results on ${}^{51}{Cr}$ and other EC decaying light nuclides, obtained mainly by bremsstrahlung- $γ$ -coincidence measurements. The transition energy of ${}^{51}{Cr}$ was determined to be 760 ± 15 keV, in good agreement with accepted atomic mass differences.

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Physical Review C

Recent Articles

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Recent Issues

Charge Asymmetry Effects and the Trinucleon Binding-Energy Difference

${}^{6}{Li} ({}^{3}{He}, t)$ Reaction and the Solar Neutrino Puzzle

Isospin-Forbidden and - Allowed ${}^{16}O (d, α) {}^{14}N$ Reactions

Neutron Polarization from ${}^{2}H (p, \vec{n})$ and ${}^{1}H (d, \vec{n})$

Generalization of the Jost Function and Its Application to Off-Shell Scattering

Analyzing Power for $d - {}^{4}{He}$ Elastic Scattering at 12.0, 14.0, and 17.0 MeV

Correlation Effects in Nuclear Densities

Separable-Interaction Model for Deuteron Breakup

Beta Decay of ${}^{17}N$

$T$ -Matrix Perturbation Theory for the Three-Nucleon System with the Reid Potential

Mesonic Second-Class Currents in Nuclear $β$ Decay

Internal Excitation and Ionization Accompanying $K$ Capture

Directional Correlations of Gamma Rays in ${}^{79}{Br}$

Accurate Masses and $β$ -Decay Schemes for ${}^{34}P$ and ${}^{33}{Si}$

Mass and $β$ Decay of the New Isotope ${}^{29}{Mg}$ : Systematics of Masses of $T_{z} = \frac{5}{2}$ Nuclides in the $2 s - 1 d$ Shell

Neutron Polarization in Isospin-Forbidden ( $p, n$ ) Reactions

Spin and Parity of ${}^{20}F$ Levels from Gamma-Ray Linear-Polarization Measurements

${}^{86, 88}{Sr} (d, {}^{3}{He}) {}^{85, 87}{Rb}$ Reactions and a Possible $Z = 38$ Magic Number

Compound-Nucleus Contribution for ( $p, α$ ) Reaction from Sn and Cd Isotopes

Radiative Capture of $S$ Electrons in the Decay of ${}^{51}{Cr}$

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