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Coulomb-nuclear interference for the ${}^{58}{Ni}$ ( ${}^{14}N$ , ${}^{14}N$ ') reaction

F. Todd Baker, T. H. Kruse, W. Hartwig, M. E. Williams, and W. Savin

Phys. Rev. C 11, 1051(R) (1975) - Published 1 March, 1975

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Interference between Coulomb and nuclear excitation has been observed for excitation of the first $2^{+}$ state of ${}^{58}{Ni}$ by inelastic scattering of ${}^{14}N$ . For classical impact parameters corresponding to "grazing collisions" the interference is strongly destructive, indicating a predominantly real nuclear form factor.

NUCLEAR REACTIONS ${}^{58}{Ni}$ ( ${}^{14}N$ , ${}^{14}N$ ), $E = 30 - 48$ MeV; measured $σ (E)$ for g.s., first $2^{+}$ state at $θ_{lab} = 59 °$ . ${}^{58}{Ni}$ ( ${}^{14}N$ , ${}^{14}N$ ), $E = 41$ MeV; measured $σ (θ)$ for g.s., first $2^{+}$ state. Enriched target.

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Separable-pair method calculation using Morse potentials

D. Goss

Phys. Rev. C 11, 1054(R) (1975) - Published 1 March, 1975

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A schematic separable-pair calculation using Morse potentials gives improved values for internal pair energies (e.g. no ${}^{4}{He}$ bound state, ${}^{6}{Li}$ excited states in close agreement with experiment). The mean square nuclear radius is related to the mean square nucleon separations as well as the external (pair c.m.) mean square radii; this provides the constraint on the external kinetic energy, which in principle allows the structure of a nucleus to be determined from the nucleon-nucleon potential. A calculation of nuclear radii from experimental binding energies and internal radii renormalized to a neutron-proton separation of 3.7 fm yields radii in qualitative agreement with experiment and provides a test of the "realism" of the potential used.

NUCLEAR STRUCTURE Separable pair method, Morse potential calculated nuclear radii for ${}^{3}H$ , ${}^{3}{He}$ , ${}^{4}{He}$ , and ${}^{6}{Li}$ .

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Observation of antiprotonic x rays in ${}^{6}{Li}$ and ${}^{4}{He}$

M. Eckhause, J. R. Kane, B. L. Roberts, R. E. Welsh, R. P. Redwine, R. E. Segel, P. D. Barnes, R. A. Eisenstein, W. C. Lam, J. Miller, R. B. Sutton, D. A. Jenkins, R. J. Powers, and A. R. Kunselman

Phys. Rev. C 11, 1056(R) (1975) - Published 1 March, 1975

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We have observed the $3 d \to 2 p$ x ray in antiprotonic atoms of ${}^{4}{He}$ . The same transition was absent in antiprotonic ${}^{6}{Li}$ but the $4 f \to 3 d$ line was present. The data are analyzed for strong interaction widths.

NUCLEAR REACTIONS Experimental antiproton absorption probabilities from atomic states in ${}^{4}{He}$ and ${}^{6}{Li}$ ; exotic atoms.

RAPID COMMUNICATION

Transition from mass asymmetry to symmetry in the spontaneous fission of Fm isotopes

M. G. Mustafa

Phys. Rev. C 11, 1059(R) (1975) - Published 1 March, 1975

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The observed transition in the spontaneous fission mass distribution from asymmetry in the lighter Fm isotopes to symmetry in the heavier Fm isotopes is studied on the basis of the potential energy surfaces (PES) and fragment shell effects in the two-center shell model. To that end, we have calculated the PES for ${}^{256}{Fm}$ and compared them with our previous PES results for other Fm isotopes. Our calculations show that the lighter Fm isotopes (up to ${}^{256}{Fm}$ ) should fission asymmetrically, while ${}^{258}{Fm}$ and other heavier Fm isotopes should fission symmetrically. This is due to the fact that the shell corrections in these nuclei are found to increase with increasing mass number and decreasing neck radius, particularly in the region beyond the second barrier. This, in turn, is a consequence of strong shell effects in fragment nuclei near the doubly closed-shell ${}_{50}^{132}{Sn}_{82}$ . The results supporting these conclusions are shown.

NUCLEAR STRUCTURE Spontaneous fission ${}^{252, 256, 258, 264}{Fm}$ ; calculated shell corrections and potential energy surfaces; asymmetric two-center shell model; transition from mass asymmetry to symmetry.

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Nuclear structure studies with ( $d, t$ ) reactions on ${}^{110}{Cd}$

K. C. Chan, B. L. Cohen, and L. Shabason

Phys. Rev. C 11, 1064(R) (1975) - Published 1 March, 1975

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Discrepancies between the energy level schemes of ${}^{109}{Cd}$ determined by radioactive decay studies and ${}^{110}{Cd} (d, t)$ reaction studies were investigated by a new study of the ${}^{110}{Cd} (d, t)$ reaction. Sixteen triton groups were found, $J^{π}$ assignments were made, and spectroscopic factors and fullnesses of single particle states were determined and compared with those for isotonic nuclei. The results remove or clarify all previous discrepancies.

NUCLEAR REACTIONS ${}^{110}{Cd} (d, t)$ , $E = 16$ MeV, measured $σ (E_{t}, θ)$ . Deduced levels in ${}^{109}{Cd}$ .

Erratum: Strong-interaction effects in antiprotonic atoms

A. Deloff and J. Law

Phys. Rev. C 11, 1067 (1975) - Published 1 March, 1975

Gamma-ray transitions in ${}^{21}{Ne}$

J. C. Lawson and P. R. Chagnon

Phys. Rev. C 11, 643 (1975) - Published 1 March, 1975

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$γ$ rays have been studied in coincidence with protons from the ${}^{19}F ({}^{3}{He}, p) {}^{21}{Ne}$ reaction. In addition to known decays, branching ratios have been measured for about 14 weak transitions. By means of $p γ$ angular-correlation experiments, spin assignments $J = \frac{1}{2} and \frac{3}{2}$ are confirmed for $E_{x} = 2789 and 3662$ keV. respectively. New spin assignments are $J = \frac{3}{2}, (\frac{3}{2}), and (\frac{9}{2})$ for $E_{x} = 4684, 5550, and 6265$ keV, respectively. Results are consistent with the unified rotational model of ${}^{21}{Ne}$ .

NUCLEAR REACTIONS ${}^{19}F ({}^{3}{He}, p γ)$ , $E_{{}^{3}{He}} = 3.5 to 7.0$ MeV; measured $p γ$ , $p γ (θ)$ . ${}^{21}{Ne}$ deduced $γ$ transitions, branching ratios. $J$ , $δ$ . Natural targets.

Classical description of the Coulomb excitation of very heavy deformed nuclei

N. Rowley and P. Colombani

Phys. Rev. C 11, 648 (1975) - Published 1 March, 1975

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Classical perturbation theory is used to obtain an idea of the "suddenness" of the Coulomb excitation of rotational levels of very heavy nuclei. Deviations from Rutherford orbits in such reactions are also estimated and found to be small. Classical values of the maximum $J$ obtainable in a given reaction are found to be in good agreement with values obtained experimentally using heavy deformed targets ( ${}^{238}U$ , ${}^{232}{Th}$ ) and heavy beams ( ${}^{132}{Xe}$ , ${}^{84}{Kr}$ ).

NUCLEAR REACTIONS Classical study of excitation of very high spin: comparison with experiments ${}^{238}U$ , ${}^{232}{Th} ({}^{84}{Kr}, {}^{84}{Kr} γ)$ and ${}^{238}U ({}^{132}{Xe}, {}^{132}{Xe} γ)$ .

Structure of ${}^{33}S$ from a study of the ${}^{34}S (p, d) {}^{33}S$ reaction at 35 MeV

A. Moalem and B. H. Wildenthal

Phys. Rev. C 11, 654 (1975) - Published 1 March, 1975

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The ${}^{34}S (p, d) {}^{33}S$ reaction has been studied at a proton energy of 35 MeV. Deuteron spectra were analyzed in a magnetic spectrograph with an over-all energy resolution, full width at half-maximum, of about 8 keV. Excitation energies were measured for levels in ${}^{33}S$ through 7.5 MeV excitation with an accuracy of ±(1.0 keV + 0.5 keV per 1 MeV of excitation). Values of the orbital angular momenta of neutrons transferred in these transitions, and the corresponding spectroscopic factors, were extracted from the data by means of distorted-wave Born-approximation calculations. Several new $J^{π} = {\frac{1}{2}}^{+}$ assignments were made. The experimental results are compared to the predictions of current nuclear structure theories for this nucleus.

NUCLEAR REACTIONS ${}^{34}S (p, d)$ , $E_{p} = 35$ MeV; measured $σ (E_{d}, θ)$ ; enriched target; deduced energies, $l_{n}$ values, and spectroscopic factors for states of ${}^{33}S$ .

Off-shell length for the two-nucleon $T$ matrix in the ${}^{3}S_{1} - {}^{3}D_{1}$ state

Michael G. Fuda

Phys. Rev. C 11, 664 (1975) - Published 1 March, 1975

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It is shown that the off-shell behavior of the low energy two-nucleon $T$ matrix, in the coupled ${}^{3}S_{1} - {}^{3}D_{1}$ state, can be characterized by a single parameter, which is the generalization from central to noncentral forces of the equivalent or off-shell length. An approximate linear relation between the square of the off-shell length and the intrinsic range, which holds for central forces, is shown to be also valid for noncentral forces. It is found that the approximate relation is exact for a separable potential of the Yamaguchi type, and hence for the unitary pole approximation.

Quasifree scattering on clustering particles and separation energies

Y. Sakamoto, P. Cüer, and F. Takéutchi

Phys. Rev. C 11, 668 (1975) - Published 1 March, 1975

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The relation between cross sections for quasifree scattering on clustering particles and separation energies of the particles in light nuclei is investigated. When the wave function for the center of mass of clustering particles relative to that of remaining ones has an oscillatory structure in the interior region, the overlap integral contains only a small contribution from this region. Consequently, the dominant contribution to the cross section will come from the asymptotic part of the wave function, which essentially depends on the binding energy of the clustering particles in the nucleus. This is a common situation in many cases of quasifree scattering on clustering particles. A theory based on this approach is able to explain the large variation in the magnitudes of a number of measured quasifree scattering cross sections.

NUCLEAR REACTIONS ${}^{6}{Li} (p, p d)$ , ( $p, p {}^{3}{He}$ ), ( $p, p α$ ), ${}^{7}{Li} (p, p d)$ , ( $p, pt$ ), ( ${}^{9}{Be} (p, p α)$ , ${}^{12}C (p, p d)$ , $E = 155 (100)$ MeV, calculated $σ (θ)$ ; ${}^{6}{Li} (π^{-}, 2 n)$ , $E = 0$ MeV, calculated recoil momentum distribution. Relation between the cross sections and separation energies.

Back-angle anomalies in alpha scattering: Inelastic scattering from the calcium isotopes

W. Trombik, K. A. Eberhard, and J. S. Eck

Phys. Rev. C 11, 685 (1975) - Published 1 March, 1975

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Cross sections for elastic and inelastic $α$ scattering on ${}^{40, 42, 44, 48}{Ca}$ have been measured to several excited states. The bombarding energy (lab) is 24 MeV for $α$ + ${}^{40, 42, 44}{Ca}$ and is 24 and 29 MeV for $α$ + ${}^{48}{Ca}$ . Particular emphasis is given to the back-angle data. In addition to the anomaly of $α$ + ${}^{40}{Ca}$ elastic scattering at backward angles previously reported by many workers anomalous features are also observed in inelastic scattering. It is found that the backward anomaly of the $α$ + ${}^{40}{Ca}$ inelastic cross sections is strongest for the $0^{+}$ states and gradually decreases with increasing spins of the final states ( $1^{-}$ , $3^{-}$ , $5^{-}$ ). The only exception is the scattering to the $2^{+}$ state at 3.90 MeV, for which the cross sections exhibit a regular decrease toward backward angles. The inelastic cross sections for the ${}^{42, 44, 48}{Ca}$ isotopes are generally smaller at backward angles as compared to those for ${}^{40}{Ca}$ . In general, the observed anomalies for inelastic scattering at back angles are in close analogy to those known for elastic scattering. An interpretation of the data and of the anomalies in terms of coupled channels is given. Both a standard optical potential and one with an angular-momentum-dependent absorption have been used in the calculations. It is found that the large differences in the cross sections at backward angles, depending on the isotope and on the spin of the residual state, can be reproduced by coupled-channel calculations when an angular-momentum-dependent absorption in the optical potential is assumed.

NUCLEAR REACTIONS ${}^{40, 42, 44, 48}{Ca} (α, α_{0})$ , ${}^{40, 42, 44, 48}{Ca} (α, α^{'})$ , $E = 24 - 29$ MeV; measured $σ (E, θ)$ ; deduced coupled-channel parameters. Enriched targets; $θ = 12.5 - 177.5 °$ , $Δ θ = 2.5 °$ ; calculated $σ (θ)$ .

Electrodisintegration of ${}^{3}{He}$

D. M. Skopik, J. J. Murphy, II, Y. M. Shin, K. F. Chong, and E. L. Tomusiak

Phys. Rev. C 11, 693 (1975) - Published 1 March, 1975

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An experimental study of the reaction ${}^{3}{He} (e, d) e^{'} p$ was carried out by measuring differential cross sections of deuterons as a function of deuteron energy and angle for three incident electron energies. The electrodisintegration cross section was also calculated using an Irving-Gunn wave function for the ground state with a plane wave for the final state. As in the case of photodisintegration calculations the result indicates the need for including complete final state rescattering effects.

NUCLEAR REACTIONS ${}^{3}{He} (e, d) e^{'} p$ , measured $σ (E_{d}, θ)$ , $E_{d} = 2.5 - 11.4$ , $θ = 30 - 150$ .

Decay schemes for high-spin states in ${}^{42}K$ and ${}^{42}{Ca}$

E. K. Warburton, J. J. Kolata, and J. W. Olness

Phys. Rev. C 11, 700 (1975) - Published 1 March, 1975

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Fusion-evaporation reactions induced by ${}^{18}O$ and ${}^{19}F$ bombardment of ${}^{26}{Mg}$ , ${}^{27}{Al}$ , and ${}^{28}{Si}$ targets with projectile energies of 20-60 MeV were used to populate high-spin states in ${}^{42}K$ and ${}^{42}{Ca}$ . Ge(Li) measurements of $γ - γ$ coincidences, together with $γ$ -ray angular distribution and linear polarization measurements, were used to establish decay schemes, excitation energies, spin-parity assignments, and $γ$ -ray transition multipolarities. These data, together with recoil-distance measurements of lifetimes, provide information also on transition strengths for the deexcitation $γ$ rays. Our results suggest assignments of $6^{+}$ and $7^{+}$ for ${}^{42}K$ levels at 1376 and 1948 keV, respectively, and indicate higher-lying levels of presumably greater spin. In ${}^{42}{Ca}$ , new odd-parity levels from $6^{-}$ to $11^{-}$ are proposed as arising from the ${d_{\frac{3}{2}}}^{- 1} {f_{\frac{7}{2}}}^{3}$ configuration.

NUCLEAR REACTIONS: ${}^{26}{Mg} ({}^{18}O, pn γ γ \dots)$ $E = 20 - 60$ MeV, ${}^{27}{Al} ({}^{18}O, 2 p n γ γ \dots)$ $E = 20 - 60$ MeV; measured $γ - γ$ coin.; deduced levels in ${}^{42}K$ , ${}^{42}{Ca}$ ; measured $σ (E_{γ}, θ)$ and $P_{γ}$ ; deduced $J^{π}$ for high-spin levels; measured recoil distance; deduced $T_{\frac{1}{2}}$ , ${| M (M L) |}^{2}$ ; confirming evidence from ${}^{19}F$ bombardment of ${}^{26}{Mg}$ and ${}^{28}{Si}$ . Enriched targets, Ge(Li) detectors.

Determination of the ${}^{12}C$ + $p$ resonance energy at 14.2 MeV

J. D. Goss, C. P. Browne, A. A. Rollefson, and P. L. Jolivette

Phys. Rev. C 11, 710 (1975) - Published 1 March, 1975

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The ${}^{12}C$ + $p$ resonance energy of the lowest $T = \frac{3}{2}$ state in ${}^{13}N$ has been determined by using the 100 cm broad-range magnetic spectrograph to measure the incident proton beam energy and a solid state detector to measure the ${}^{12}C (p, p) {}^{12}C$ yield curve. Phase-shift analyses of 10 proton elastic scattering yield curves taken at a laboratory observation angle of 160° give a value of the ${}^{12}C$ + $p$ resonance energy of 14.2325±0.0022 MeV. We compare our result with that of a recent time-of-flight measurement (14.230 75 ± 0.000 20 MeV) and conclude that the nuclear-reaction energy scale based on the ${}^{210}{Po} (α)$ energy is in agreement with the absolute measurement against the meter and second to within an uncertainty of better than 0.016%.

NUCLEAR REACTIONS ${}^{12}C (p, p_{0}) {}^{12}C$ , measured 14.23 MeV $T = \frac{3}{2}$ resonance energy. Compared energy scales.

Phenomenological absorption model for pion-nucleus scattering

P. A. Kazaks and J. A. Smith

Phys. Rev. C 11, 715 (1975) - Published 1 March, 1975

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A phenomenological model is used to obtain cross sections for 120-230 MeV pions elastically scattered from ${}^{12}C$ . The model wave function consists of a diffuse hole cut out of a plane wave and a focus term. Three parameters in the focus term are varied to fit the experimental cross sections. The focus is found to be essential but diminishing in strength up to 200 MeV. It then becomes very weak. Good fits are obtained with this very simple procedure. It can be used to readily obtain the simplest kind of distorted pion wave.

NUCLEAR REACTIONS ${}^{12}C (π, π)$ , $E = 120 - 230$ MeV; calculated $σ (θ)$ : Absorption model with fitted focus term.

Analysis of three-body final states: Nonrelativistic

R. D. Amado

Phys. Rev. C 11, 719 (1975) - Published 1 March, 1975

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Quantum mechanics forces rapid variation and coherent interrelation on amplitudes usually taken to be independent and constant in the Watson approximation to final state interactions. These effects are particularly important when more than one pair of final state interactions is simultaneously big. We develop these amplitude conditions using unitarity only. We show how these constraints combined with analyticity give a set of linear scattering integral equations. These equations are not only the minimal set compatible with the general constraints of quantum mechanics, but also turn out to be the simplest form of the separable interaction equations.

${}^{16, 18}O (α, {}^{6}{He}) {}^{14, 16}O$ reactions

A. VanderMolen, F. D. Becchetti, J. Jänecke, and L. Chua

Phys. Rev. C 11, 734 (1975) - Published 1 March, 1975

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The ( $α$ , ${}^{6}{He}$ ) reaction on ${}^{16}O$ and ${}^{18}O$ has been studied at $E_{α} = 58$ MeV. Although the cross sections are much smaller than the corresponding ( $p, t$ ) cross sections by about a factor of 20, the angular distributions are characteristic of a direct transfer mechanism and are reproduced satisfactorily by distorted-wave theory assuming $LS$ coupling in ${}^{6}{He}$ .

NUCLEAR REACTIONS: ${}^{16}O (α, {}^{6}{He})$ and ${}^{18}O (α, {}^{6}{He})$ , $E = 58$ MeV; measured $σ (E_{{}^{6}{He}}, θ)$ ; ${}^{16}O$ deduced transition strengths and DWBA normalization.

$E 0$ decay of the first excited $0^{+}$ state in ${}^{32}S$

J. C. Adloff, K. H. Souw, D. Disdier, and P. Chevallier

Phys. Rev. C 11, 738 (1975) - Published 1 March, 1975

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The $E 0$ branching ratio $\frac{Γ_{π}}{Γ}$ of the ${}^{32}S$ (3.78-MeV, $0^{+}$ ) state to the ground state was measured to be (3.54 ± 0.62) × $10^{- 4}$ . When combined with the lifetime $τ_{m} = (0.90 \pm 0.15)$ psec of this state one obtains the value ${〈 M 〉}_{π} = (2.22 \pm 0.27)$ ${fm}^{2}$ for the $E 0$ matrix element.

NUCLEAR REACTION ${}^{31}P ({}^{3}{He}, d)$ , $E = 8.5$ MeV; ${}^{32}S$ measured $E 0$ branching ratio. Deduced $E 0$ matrix element.

Electromagnetic transitions in ${}^{22}{Na}$

R. H. Spear, R. A. I. Bell, M. T. Esat, P. R. Gardner, D. C. Kean, and A. M. Baxter

Phys. Rev. C 11, 742 (1975) - Published 1 March, 1975

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Electromagnetic properties of excited states of ${}^{22}{Na}$ below 4.6-MeV excitation energy have been studied using the ${}^{23}{Na} ({}^{3}{He}, α γ) {}^{22}{Na}$ and ${}^{19}F (α, n γ) {}^{22}{Na}$ reactions. Investigation of the decay scheme of the 4069-keV level using the ${}^{23}{Na} ({}^{3}{He}, α γ) {}^{22}{Na}$ reaction shows a (10 ± 3)% branch to the 1528-keV level, compared to a value of 21% reported previously. The existence of weak $γ$ -ray transitions from the 1983-, 2211-, and 2572-keV levels has been confirmed from $γ$ -ray spectra obtained above and below threshold for population of these levels via the ${}^{19}F (α, n) {}^{22}{Na}$ reaction. A long standing controversy regarding the spin of the 1983-keV level has been resolved by $γ$ -ray angular distribution measurements close to threshold for the population of the 1983-keV level via the ${}^{19}F (α, n) {}^{22}{Na}$ reaction; the results show that $J^{π} (1983) = 3^{+}$ . Neutron- $γ$ correlation studies of the ${}^{19}F (α, n γ) {}^{22}{Na}$ reaction, taken in conjunction with previous data, impose limitations on spins and parities of several levels and on mixing ratios of associated $γ$ -ray transitions. The spin-parity values are as follows, relatively unlikely assignments being bracketed: $J^{π} (3708) = 6^{+} (4^{\pm})$ ; $J^{π} (4069) = 4^{+}$ ; $J^{π} (4466) = 1^{-}, 2^{\pm}, 3^{-}, or 4^{-}$ ; $J^{π} (4522) = 7^{+}, 5^{\pm} (4^{-}, 6^{+})$ .

NUCLEAR REACTIONS ${}^{23}{Na} ({}^{3}{He}, α γ)$ , $E = 8.46$ MeV; measured $σ (E_{α}, E_{γ})$ . ${}^{22}{Na}$ level deduced $γ$ branching. ${}^{19}F (α, n γ)$ , $E = 4.7 - 6.1$ MeV; measured $σ (E, E_{γ})$ . ${}^{22}{Na}$ levels deduced $γ$ branching. ${}^{19}F (α, n γ)$ , $E = 5.0 - 5.2$ MeV; measured $σ (E_{γ}, θ)$ . ${}^{22}{Na}$ level deduced $J$ , $π$ , $δ$ . ${}^{19}F (α, n γ)$ , $E = 11.2$ MeV; measured $σ (E_{n}, E_{γ}, θ_{n γ})$ . ${}^{22}{Na}$ deduced levels; ${}^{22}{Na}$ levels deduced $J$ , $π$ , $δ$ , $τ$ .

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Coulomb-nuclear interference for the ${}^{58}{Ni}$ ( ${}^{14}N$ , ${}^{14}N$ ') reaction

Separable-pair method calculation using Morse potentials

Observation of antiprotonic x rays in ${}^{6}{Li}$ and ${}^{4}{He}$

Transition from mass asymmetry to symmetry in the spontaneous fission of Fm isotopes

Nuclear structure studies with ( $d, t$ ) reactions on ${}^{110}{Cd}$

Erratum: Strong-interaction effects in antiprotonic atoms

Gamma-ray transitions in ${}^{21}{Ne}$

Classical description of the Coulomb excitation of very heavy deformed nuclei

Structure of ${}^{33}S$ from a study of the ${}^{34}S (p, d) {}^{33}S$ reaction at 35 MeV

Off-shell length for the two-nucleon $T$ matrix in the ${}^{3}S_{1} - {}^{3}D_{1}$ state

Quasifree scattering on clustering particles and separation energies

Back-angle anomalies in alpha scattering: Inelastic scattering from the calcium isotopes

Electrodisintegration of ${}^{3}{He}$

Decay schemes for high-spin states in ${}^{42}K$ and ${}^{42}{Ca}$

Determination of the ${}^{12}C$ + $p$ resonance energy at 14.2 MeV

Phenomenological absorption model for pion-nucleus scattering

Analysis of three-body final states: Nonrelativistic

${}^{16, 18}O (α, {}^{6}{He}) {}^{14, 16}O$ reactions

$E 0$ decay of the first excited $0^{+}$ state in ${}^{32}S$

Electromagnetic transitions in ${}^{22}{Na}$

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