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Coulomb excitation of ${}^{125}{Te}$

J. Barrette, M. Barrette, R. Haroutunian, G. Lamoureux, S. Monaro, and S. Markiza

Phys. Rev. C 11, 282(R) (1975) - Published 1 January, 1975

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The properties of the low-lying levels of ${}^{125}{Te}$ were investigated by the Coulomb excitation process which was effected by bombarding a thick natural tellurium target with 9.5- and 10.5-MeV $α$ particles and a thick target of isotopically enriched ${}^{125}{Te}$ (95%) with 45-MeV ${}^{16}O$ ions. Levels at 443.58, 463.39, 671.42, and 729.30 MeV were Coulomb excited and the reduced upward transition probabilities $B (E 2 ↑)$ ( $e^{2} b^{2}$ ) extracted from the data were: 0.186 ± 0.005, 0.158 ± 0.005, 0.130 ± 0.004, and 0.0059 ± 0.0008. Angular distribution measurements were performed with 42-MeV ${}^{16}O$ ions. The following results were obtained for the $γ$ rays deexciting the 443.58- ( $\frac{3}{2^{+}}$ ) keV level: $δ (408.10) = + 0.41 (5) or + 1.35 (12)$ , $δ (443.58) = + 0.14 (4) or - 2.4 (3)$ .

NUCLEAR REACTIONS ${}^{125}{Te} (α, α^{'} γ)$ , $E = 9.5 - 10.5$ MeV; ${}^{125}{Te} ({}^{16}O, {}^{16}O^{'} γ)$ , $E = 42 - 45$ MeV, ${}^{125}{Te}$ deduced levels, $B (E 2)$ $B (M 1)$ , $τ$ , $J$ , $π$ , $γ$ branching. Enriched and natural targets.

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Enhanced excitation of the outgoing particle in the ${}^{27}{Al}$ ( ${}^{12}C$ , ${}^{11}B$ ) ${}^{28}{Si}$ reaction

F. Pougheon, P. Roussel, C. Détraz, and G. Rotbard

Phys. Rev. C 11, 287(R) (1975) - Published 1 January, 1975

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The semiclassical description of heavy-ion induced transfer reactions is used to select a case in which ejectile excitation should be enhanced. The ground-state transition in the ${}^{27}{Al}$ ( ${}^{12}C$ , ${}^{11}B$ ) ${}^{28}{Si}$ reaction is found to exhibit such an effect.

NUCLEAR REACTIONS ${}^{27}{Al}$ ( ${}^{12}C$ , ${}^{11}B$ ), $E ({}^{12}C) = 46.5$ MeV, measured $σ (E ({}^{11}B), θ)$ .

Two-body photodisintegration of ${}^{3}{He}$ and ${}^{3}H$

B. F. Gibson and D. R. Lehman

Phys. Rev. C 11, 29 (1975) - Published 1 January, 1975

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Cross sections for two-body photodisintegration of ${}^{3}{He}$ and ${}^{3}H$ are calculated in electric-dipole approximation. The calculation is performed within the context of exact three-body theory with the two-nucleon interactions represented by $s$ -wave spin-dependent separable potentials fitted to the low-energy nucleon-nucleon scattering data. The two-body photo-disintegration amplitude is expressed in terms of the half-off-shell nucleon plus correlated-pair amplitudes, a method applicable to any weak-process disintegration amplitude. The numerical results indicate: (1) The ${}^{3}{He}$ and ${}^{3}H$ 90° photodisintegration cross sections are essentially identical in shape, being only slightly displaced at low energy due to the different thresholds, when both initial and final states are treated consistently. (2) The ${}^{3}{He} (γ, d) p$ 90° differential cross section has a peak value of approximately 95 μb/sr.

NUCLEAR REACTIONS Photodisintegration of ${}^{3}{He}$ and ${}^{3}H$ ; exact three-body calculation; separable potentials; charge-dependent interactions.

New coupled-reaction-channels formalism for nuclear reactions

W. Tobocman

Phys. Rev. C 11, 43 (1975) - Published 1 January, 1975

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A set of coupled integral equations (CIE) for multichannel nuclear reactions is considered which appears to have some advantages over the conventional coupled-reaction-channel (CRC) equations when transfer channels must be included. Both the CIE and CRC formalism are based on the assumption that the system has a limited number of cluster type intermediate states available to it. The CIE have a connected kernel while those of the CRC do not. In addition, the troublesome nonorthogonality terms of the CRC formalism have no counterpart in the CIE formalism. The CIE are compared with those of the CRC formalism. The CIE for a simple model for deuteron scattering from a structureless target are presented as an explicit example.

NUCLEAR REACTIONS Coupled-reaction-channels formalism with no nonorthogonality term and having a connected kernel.

Excitation functions for ${}^{7}{Be}$ production by light-ion bombardment of ${}^{12}C$

C. B. Fulmer and D. A. Goldberg

Phys. Rev. C 11, 50 (1975) - Published 1 January, 1975

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We have measured excitation functions for production of ${}^{7}{Be}$ by $d$ -, ${}^{3}{He}$ -, and $α$ -particleinduced reactions in carbon using the stacked-foil method. Similar measurements for protons were obtained earlier. For each particle the data extend beyond 75 MeV. The ${}^{7}{Be}$ yields approach zero, respectively, in the neighborhood of threshold energies for the ( $p$ , ${}^{6}{Li}$ ), ( $d$ , ${}^{7}{Li}$ ), ( ${}^{3}{He}$ , ${}^{8}{Be}$ ), and ( $α$ , ${}^{9}{Be}$ ) reactions. The $p$ - and ${}^{3}{He}$ -induced yields have similar energy dependences, peaking at roughly 10 MeV above threshold; in contrast, the maximum cross sections for the $d$ and $α$ curves occur 30-50 MeV above threshold energies. The maximum yield from ${}^{3}{He}$ -induced reactions (98 mb) is about a factor of 3 larger than that for $p$ , $d$ , or $α$ . These results suggest that $α$ -particle pickup may be an important part of the ${}^{7}{Be}$ yield at the lower energy part of the ${}^{3}{He}$ excitation function.

NUCLEAR REACTIONS ${}^{12}C (d, x)$ , ${}^{12}C ({}^{3}{He}, x)$ , ${}^{12}C (α, x)$ ; $E \sim 20 - 80$ MeV; measured $σ (E)$ ; Ge(Li) detector. Deduced reaction mechanism.

${}^{29}{Si} (α, n) {}^{32}S$ reaction from 2.15 to 5.25 MeV bombarding energy

M. Balakrishnan, M. K. Mehta, A. S. Divatia, and S. Kailas

Phys. Rev. C 11, 54 (1975) - Published 1 January, 1975

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Levels in the compound nucleus ${}^{33}S$ have been investigated by measuring the reaction cross section for the reaction ${}^{29}{Si} (α, n) {}^{32}S$ for incident $α$ energies from 2.15 to 5.25 MeV, mostly in steps of 2.5 keV, using a $4 π$ -geometry neutron counter. One hundred and thirty-four resonances have been identified. The reciprocity theorem has been used to calculate the total cross section for the inverse reaction ${}^{32}S (n, α) {}^{29}{Si}$ . Total widths have been determined for 107 resonances, and partial widths $Γ_{α}$ , $Γ_{n}$ and corresponding reduced widths ${γ_{α}}^{2}$ , ${γ_{n}}^{2}$ have been extracted for 19 cases where spin values are known. Statistical strength function analysis of the cross section under the excitation curve gave the averaged $α$ particle strength function value as $〈 {\bar{S}}_{α} 〉 = 0.067 \pm 0.012$ for this reaction.

NUCLEAR REACTIONS ${}^{29}{Si} (α, n)$ , $E = 2.15 - 5.25$ MeV; measured $σ (E)$ ; ${}^{33}S$ levels, deduced $Γ_{α}$ , $Γ_{n}$ , $S$ . $σ$ ${}^{32}S (n, α)$ reaction, reciprocity theorem; statistical analysis, deduced ${\bar{S}}_{α}$ .

Mechanism of ( $p, t$ ) and ( $p$ , ${}^{3}{He}$ ) reactions by the analysis of the energy dependence of mirror transitions

S. Micheletti, M. Pignanelli, and P. Guazzoni

Phys. Rev. C 11, 64 (1975) - Published 1 January, 1975

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The reactions ${}^{13}C (p, t) {}^{11}C$ , ${}^{13}C (p, {}^{3}{He}) {}^{11}B$ , ${}^{16}O (p, t) {}^{14}O$ , and ${}^{16}O (p, {}^{3}{He}) {}^{14}N$ have been studied at several incident energies between 24 and 44 MeV. Previous results on the ${}^{15}N (p, t) {}^{13}N$ and ${}^{15}N (p, {}^{3}{He}) {}^{13}C$ reactions are also considered in the analysis. The energy dependence of cross section ratios for mirror transitions evidences that these reactions cannot be described below 35-40 MeV simply as a direct two-nucleon pickup. The values for spin and isospin dependent terms in the effective interactions obtained from a distorted-wave Born-approximation analysis differ from those used in shell model calculations and in microscopic analyses of inelastic scattering.

NUCLEAR REACTIONS ${}^{13}C (p, t)$ , ( $p$ , ${}^{3}{He}$ ), $E = 26.8 - 43.1$ MeV; measured $σ (E_{t}, θ)$ , $σ (E_{{}^{3}{He}}, θ)$ ; $θ_{lab} = 10 - 72.5 °$ . ${}^{16}O (p, t)$ , ( $p$ , ${}^{3}{He}$ ), $E = 32.2, 36.6, 43.5$ MeV; measured $σ (E_{t}, θ)$ , $σ (E_{{}^{3}{He}}, θ)$ , $θ_{lab} = 10 - 82.5 °$ ; resolution 200 keV. Reaction mechanism analysis.

Pion-nucleus scattering in a cluster model

Ying-Yeung Yam

Phys. Rev. C 11, 73 (1975) - Published 1 January, 1975

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The forward amplitude for pion-nucleus scattering in the $N^{*}$ region is studied using a Glauber formalism with a cluster model of the nucleus. It is found that the major features of the data for light nuclei ( ${}^{6}{Li}$ , ${}^{7}{Li}$ , ${}^{9}{Be}$ , ${}^{12}C$ , ${}^{16}O$ ) are reasonably well reproduced by using a simple parametrization of the cluster structure. These results are in sharp contrast to predictions of a nucleon model at a comparable level of simplicity. We argue that a Glauber series representation of the amplitude is viable in a cluster model but not reliable in a nucleon model essentially because the interlocking effects of multiple scatterings and strong particle correlations inside the nucleus are easy to approximate in the former model and are difficult to account for in the latter model. Several modifications of the basic cluster model are considered and estimated to be small. More studies, experimental and theoretical, on angular distributions are urged.

NUCLEAR REACTION ${}^{2}H$ , ${}^{3}{He}$ , ${}^{4}{He}$ , ${}^{6}{Li}$ , ${}^{7}{Li}$ , ${}^{9}{Be}$ , ${}^{12}C$ , ${}^{16}O$ , ${}^{27}{Al}$ , ${}^{32}S$ ; forward amplitude in the $N^{*}$ region calculated with a cluster model using a Glauber approximation and compared to data.

Nuclear viscosity

B. Giraud, J. Le Tourneux, and E. Osnes

Phys. Rev. C 11, 82 (1975) - Published 1 January, 1975

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Jost function for coupled partial waves of the Reid soft-core potential

T. Sasakawa and T. Sawada

Phys. Rev. C 11, 87 (1975) - Published 1 January, 1975

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MILESTONE

Extraction of $a_{nn}$ from the reaction $π^{-} d \to γ nn$

W. R. Gibbs, B. F. Gibson, and G. J. Stephenson, Jr.

Phys. Rev. C 11, 90 (1975) - Published 1 January, 1975

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Extraction of a value for the neutron-neutron scattering length by an analysis of the reaction $π^{-} + d \to γ + n + n$ necessitates making assumptions about the reaction amplitude. We have studied the sensitivity of the extracted value of $a_{nn}$ to such an analysis by performing a series of theoretical experiments in which a standard set of assumptions is used to analyze data generated by variations in one or more of these assumptions. For kinematically complete experiments the major sources of uncertainty lie in the energy dependence of the short-range characterization of the $n - n$ final-state wave function and to a lesser extent the treatment of the pion wave function in the initial state. We conclude that a value of $a_{nn}$ can be extracted from this experiment with a theoretical uncertainty of less than 0.3 fm.

NUCLEAR REACTIONS $π^{-} (d, n n) γ$ , scattering length extraction, deuteron wave function, $nn$ wave function neutron time-of-flight spectra.

Study of the ${}^{84}{Kr} ({}^{3}{He}, d) {}^{85}{Rb}$ reaction

L. R. Medsker, J. N. Bishop, S. C. Headley, and H. T. Fortune

Phys. Rev. C 10, 2117 (1974) - Published 1 December, 1974

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The ${}^{84}{Kr} ({}^{3}{He}, d) {}^{85}{Rb}$ reaction has been studied at a bombarding energy of 18 MeV. The isotopically enriched ${}^{84}{Kr}$ target was contained in a gas cell with no entrance window. Excitation energies and angular distributions were obtained for 58 levels below $E_{x} = 6.2$ MeV in ${}^{85}{Rb}$ . A distorted-wave analysis was used to determine $l$ values and spectroscopic strengths. The results are compared with previous data from transfer reactions and radioactive decay.

NUCLEAR REACTIONS ${}^{84}{Kr} ({}^{3}{He}, d)$ , $E = 18$ MeV; enriched target; measured $σ (E_{d}, θ)$ ; deduced ${}^{85}{Rb}$ levels, $l$ , $j$ , $G_{lj}$ .

Pion-nucleus charge exchange reactions in the isobar-doorway model

M. A. Nagarajan and W. L. Wang

Phys. Rev. C 10, 2125 (1974) - Published 1 December, 1974

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The isobar-doorway model, previously applied to the study of pion-nucleus elastic scatterings, is generalized to the treatment of single and double charge exchange reactions. The charge exchange amplitudes are calculated within the framework of distorted-wave Born approximation, where the resonant distortion of the elastic scattering wave functions in the initial and final channels as well as the resonant part of the charge exchange interaction are explicitly taken into account. In the isobar-doorway model, it is shown that the transition amplitude depends upon quantities related to the elastic scattering and to a charge exchange amplitude which contains nonresonant initial and final pion wave functions. The strong energy dependence in various components of single and double charge exchange amplitudes is clearly displayed in the model; this energy dependence due to the (3,3) isobar in the reaction mechanism (including initial- and final-state interactions) may also be separated out from the nuclear structure information as contained in the nuclear form factors. This separation is obtained through the static and the closure approximations which are in the isobar-doorway model.

NUCLEAR REACTIONS Pion-nucleus charge exchange; (3,3) resonance; isobar-doorway model.

Is there a superband in ${}^{20}{Ne}$ ?

H. T. Fortune, R. R. Betts, and R. Middleton

Phys. Rev. C 10, 2135 (1974) - Published 1 December, 1974

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No evidence is found in the ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$ reaction for a $6^{+}$ member of a "superband" predicted by Vogt to lie in the range $E_{x} = 10 - 11$ MeV. We suggest the $6^{+}$ state at 12.14 MeV as the $6^{+}$ member of the core-excited band built on the 7.20-MeV $0^{+}$ state.

NUCLEAR REACTIONS ${}^{12}C ({}^{12}C, α) {}^{20}{Ne}$ , $E = 30 - 37$ MeV. Measured $σ [E ({}^{12}C), E_{α}]$ . $θ_{lab} = 3.75 °$ .

Neutron resonance spectroscopy: Chlorine

U. N. Singh, H. I. Liou, G. Hacken, M. Slagowitz, F. Rahn, J. Rainwater, W. Makofske, and J. B. Garg

Phys. Rev. C 10, 2138 (1974) - Published 1 December, 1974

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Results are presented of time of flight total $σ$ vs $E$ measurements for natural Cl to 400 keV. Resonance parameters were obtained for 35 resonances below 200 keV. Of these, 12 resonances were assigned to ${}^{35}{Cl}$ , 6 to ${}^{37}{Cl}$ , with 17 weak resonances for which isotope assignments could not be made. On the basis of our assignments as $s$ or $p$ resonances, $10 {}^{4}S_{0} = ({0.12}_{- 0.07}^{+ 0.23})$ for ${}^{35}{Cl}$ and ( ${0.59}_{- 0.28}^{+ 0.66}$ ) for ${}^{37}{Cl}$ . For ${}^{35}{Cl}$ , $10 {}^{4}S_{1} = ({0.77}_{- 0.29}^{+ 0.53})$ with no $S_{1}$ determination for ${}^{37}{Cl}$ . The anomalous behavior of $σ$ vs $E$ below ∼ 1000 eV for natural Cl, along with previously established thermal cross sections, are fitted by assigning a bound resonance in ${}^{35}{Cl}$ at - 130 eV, having $l = 0$ , $J = 2$ , $Γ_{n}^{0} = 0.725$ eV, and $Γ_{γ} = 0.378$ eV.

NUCLEAR REACTIONS ${}^{35, 37}{Cl} (n, n)$ , ( $n, γ$ ), $E = 20 eV - 400 keV$ ; measured $σ_{t} (E)$ ; deduced $E_{0}$ , $ag Γ_{n}$ , $l$ , $J$ , $S_{0}$ , $S_{1}$ .

Neutron resonance spectroscopy: Calcium

U. N. Singh, H. I. Liou, J. Rainwater, G. Hacken, W. Makofske, and J. B. Garg

Phys. Rev. C 10, 2143 (1974) - Published 1 December, 1974

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Results are presented to 550 keV of high resolution time of flight neutron total cross section measurements using various sample thicknesses of natural calcium. An $R$ -matrix analysis was made to fit the results for the nine strong $s$ levels in ${}^{40}{Ca}$ above 100 keV. A transmission area analysis was made for the 22 weaker observed levels which are also mainly due to ${}^{40}{Ca}$ , but have $l > 0$ . We obtain $10 {}^{4}S_{0} = ({2.97}_{- 1.05}^{+ 1.95})$ for ${}^{40}{Ca}$ .

NUCLEAR REACTIONS ${}^{40}{Ca} (n, n)$ , ( $n, γ$ ), $E = 0 - 550$ keV; measured $σ_{t} (E)$ ; deduced $E_{0}$ , $Γ_{n}$ , ag $Γ_{n}$ , $S_{0}$ .

Neutron resonance spectroscopy: Fluorine

U. N. Singh, H. I. Liou, J. Rainwater, G. Hacken, and J. B. Garg

Phys. Rev. C 10, 2147 (1974) - Published 1 December, 1974

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Results are reported of high resolution transmission measurements on Teflon, ${(C F_{2})}_{n}$ , for the total cross section of natural fluorine vs energy from 500 eV to 200 keV. This region has three strong $l = 1$ levels which were fitted using a multilevel $R$ -matrix analysis. The best fit ( $E_{0}, J, Γ_{n}$ ) parameters are (26.99, 2, 0.325), (48.78, 1, 1.67), and (97.50, 1, 14.5), where $E_{0}$ and $Γ_{n}$ are in keV. The results are consistent with previous measurements. They yield $10 {}^{4}S_{1} = ({11.1}_{- 5.2}^{+ 12.4})$ for ${}^{19}F$ using a 5 fm channel redius.

NUCLEAR REACTIONS ${}^{19}F (n, n)$ , $n, γ$ , $E = 500 eV - 200 keV$ ; measured $σ_{t} (E)$ ; deduced $E_{0}$ , $l$ , $J$ , $Γ_{n}$ , $S_{1}$ .

Neutron resonance spectroscopy: Magnesium

U. N. Singh, H. I. Liou, J. Rainwater, G. Hacken, and J. B. Garg

Phys. Rev. C 10, 2150 (1974) - Published 1 December, 1974

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The total neutron cross sections vs energy to 500 keV, measured using high purity samples of nutural Mg, show four main strong levels plus a weak level at 498 keV. An $R$ -matrix fit is mainly established by the four strong levels having ( $E_{0}, A, l, J, Γ_{n}$ ) values (19.90, 25, 0, 2, 1.79 ± 0.18), (83.50, 24, 1, 3/2, 7.6 ± 0.5), (265.2, 24, 1, 1/2, 90 ± 5), and (426.3, 24, 1, 3/2, 23.2 ± 2.3), with $E_{0}$ and $Γ_{n}$ in keV. Using a channel radius of 5 fm, we obtain a $p$ strength function for ${}^{24}{Mg}$ , $10 {}^{4}S_{1} = ({10.5}_{- 4.9}^{+ 11.8})$ to 500 keV.

NUCLEAR REACTIONS $Mg (n, n)$ , $n, γ$ , $E = \sim 4 eV - 500 keV$ ; measured $σ_{t} (E)$ ; deduced $E_{0}$ , $l$ , $J$ , $Γ_{n}$ , $S_{1}$ .

Target correlations in the continuous ( $d, {}^{3}{He}$ ) reaction spectrum

George L. Strobel

Phys. Rev. C 10, 2153 (1974) - Published 1 December, 1974

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The ( $d, {}^{3}{He}$ ) reaction spectrum is calculated in a plane wave one-step direct reaction model. Target correlations due to a residual interaction are included. The discrete spectrum is dominated by the continuous spectra, at energies where both contribute. As a result the comparatively smooth experimental spectra can be understood in this reaction model.

NUCLEAR REACTICNS ${}^{12}C (d, {}^{3}{He})$ calculated ${}^{3}{He}$ spectrum.

Total cross sections for the ${}^{19}F$ ( ${}^{13}C$ , ${}^{12}C$ ) ${}^{20}F$ and ${}^{23}{Na}$ ( ${}^{13}C$ , ${}^{12}C$ ) ${}^{24}{Na}$ reactions

H. Laumer and G. G. Seaman

Phys. Rev. C 10, 2159 (1974) - Published 1 December, 1974

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Total cross sections for the ( ${}^{13}C$ , ${}^{12}C$ ) reaction on ${}^{19}F$ at laboratory energies of 9.0 to 25.0 MeV and on ${}^{23}{Na}$ at energies of 10.5 to 19.5 MeV were measured by detecting the $γ$ rays from excited states and from the decay of the radioactive ground states. At energies well below the Coulomb barrier the cross sections are compared with a semiclassical distorted wave Born approximation calculation, and spectroscopic factors are extracted.

NUCLEAR REACTIONS ${}^{19}F$ ( ${}^{13}C$ , ${}^{12}C$ ), $E = 9 - 25$ MeV; ${}^{23}{Na}$ ( ${}^{13}C$ , ${}^{12}C$ ), $E = 10.5 - 19.5$ MeV; measured $γ$ yields. ${}^{20}F$ , ${}^{24}{Na}$ levels deduced $σ (E)$ , $S$ . Coulomb DWBA analysis.

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Coulomb excitation of ${}^{125}{Te}$

Enhanced excitation of the outgoing particle in the ${}^{27}{Al}$ ( ${}^{12}C$ , ${}^{11}B$ ) ${}^{28}{Si}$ reaction

Two-body photodisintegration of ${}^{3}{He}$ and ${}^{3}H$

New coupled-reaction-channels formalism for nuclear reactions

Excitation functions for ${}^{7}{Be}$ production by light-ion bombardment of ${}^{12}C$

${}^{29}{Si} (α, n) {}^{32}S$ reaction from 2.15 to 5.25 MeV bombarding energy

Mechanism of ( $p, t$ ) and ( $p$ , ${}^{3}{He}$ ) reactions by the analysis of the energy dependence of mirror transitions

Pion-nucleus scattering in a cluster model

Nuclear viscosity

Jost function for coupled partial waves of the Reid soft-core potential

Extraction of $a_{nn}$ from the reaction $π^{-} d \to γ nn$

Study of the ${}^{84}{Kr} ({}^{3}{He}, d) {}^{85}{Rb}$ reaction

Pion-nucleus charge exchange reactions in the isobar-doorway model

Is there a superband in ${}^{20}{Ne}$ ?

Neutron resonance spectroscopy: Chlorine

Neutron resonance spectroscopy: Calcium

Neutron resonance spectroscopy: Fluorine

Neutron resonance spectroscopy: Magnesium

Target correlations in the continuous ( $d, {}^{3}{He}$ ) reaction spectrum

Total cross sections for the ${}^{19}F$ ( ${}^{13}C$ , ${}^{12}C$ ) ${}^{20}F$ and ${}^{23}{Na}$ ( ${}^{13}C$ , ${}^{12}C$ ) ${}^{24}{Na}$ reactions

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