Distorted-wave Born Approximation Analysis Research Articles

Zero-range distorted-wave Born approximation analysis of (p,t) transfer reactions

Zero-range distorted-wave Born approximation calculations are used to investigate the systematics of two-nucleon transfer reactions. The shapes of the calculated 40Ca(t,p)42Ca(gs) and 208Pb(p,t)206Pb(gs) cross sections are relatively insensitive to details of the core plus two-neutron form factor, if the form factor tails have similar shapes. Studies of heavy targets such as 206Pb suggest a surface reaction mechanism, but lighter targets (16O and 40Ca) indicate that spatial regions beyond the target surface provide the dominant contribution to the (p,t) cross section.

(t,d) reaction onTe124,Te126,Te128, andTe130nuclei

Differential cross section angular distributions have been measured for levels below 2.5 MeV in each residual nucleus in the $^{124,126,128,130}\mathrm{Te}(t,d)^{125,127,129,131}\mathrm{Te}$ reactions at ${E}_{t}=16$ MeV. The reaction products were analyzed in an Enge split-pole magnetic spectrograph and were detected by a delay-line counter at the focal plane. The deuteron energy resolution obtained was between 13 and 15 keV full width at half maximum depending on the target used. The deuteron spectra from these $\mathrm{Te}(t,d)$ reactions are quite similar to the proton spectra obtained in the ($d,p$) reactions on the same target nuclei. Several new levels were, however, populated and most of them have $L$ values \ensuremath{\ge}2. Distorted-wave Born-approximation analyses of these $\mathrm{Te}(t,d)$ reaction data have been performed and spectroscopic factors extracted. These compare well with the spectroscopic factors obtained from previous ($d,p$) experiments except for levels in $^{125}\mathrm{Te}$. In this case the present values are \ensuremath{\sim}25% lower than those obtained in the ($d,p$) reaction; however, they are in good agreement with the spectroscopic factors obtained in ($t,d$) and ($d,p$) reactions on the other tellurium nuclei.NUCLEAR REACTIONS $^{124,126,128,130}\mathrm{Te}(t,d)^{125,127,129,131}\mathrm{Te}$, ${E}_{t}=16$ MeV, measured $\ensuremath{\sigma}({E}_{d},\ensuremath{\theta})$, resolution 13-15 keV, DWBA calculations, deduced $L$ transfers, spectroscopic factors.

Ca48(d, n)Sc49reaction atEd=20MeV; proton single-particle states inSc49

The $^{48}\mathrm{Ca}(d, n)^{49}\mathrm{Sc}$ reaction has been studied at ${E}_{d}=20$ MeV. Angular distributions of differential cross sections have been obtained for 14 transitions to states in $^{49}\mathrm{Sc}$ up to an excitation energy of 7.1 MeV. A distorted-wave Born-approximation analysis has been made of the experimental data. With respect to states corresponding to the same proton single-particle orbital, relative values of derived spectroscopic factors are generally in good agreement with those obtained from ($^{3}\mathrm{He}$, $d$) reaction data. There are remarkable differences between the results from the $^{48}\mathrm{Ca}(d, n)^{49}\mathrm{Sc}$ reaction and the $^{48}\mathrm{Ca}(^{3}\mathrm{He}, n)^{49}\mathrm{Sc}$, however, regarding the dependence of the relative spectroscopic factors on proton single-particle orbitals.NUCLEAR REACTIONS $^{48}\mathrm{Ca}(d, n)^{49}\mathrm{Sc}$, $E=20$ MeV, neutron time of flight, $\ensuremath{\Delta}E=120$ keV. Measured differential cross sections, 7.5\ifmmode^\circ\else\textdegree\fi{}-50\ifmmode^\circ\else\textdegree\fi{} lab. DWBA analysis, derived spectroscopic factors.

Finite range distorted-wave Born approximation analysis of (p,t) reactions with a realistic triton wave function

Exact finite range distorted-wave Born approximation analysis of the ground state reactions $^{208}\mathrm{Pb}$($p$,$t$)$^{206}\mathrm{Pb}$ and $^{18}\mathrm{O}$($p$,$t$)$^{16}\mathrm{O}$ are presented. The calculations are carried out using a realistic triton wave function comprising a spatially symmetric $S$ and mixed symmetric ${S}^{\ensuremath{'}}$ and $D$ states. The transfer interaction is treated consistently with the interaction used in obtaining the triton wave function. The use of a realistic wave function and transfer potential yields improved agreement between experimental and theoretical angular distributions. Calculations using the wave function of the transferred neutron pair suggest it is possible to explain both the absolute magnitude and shape of the angular distribution for these transitions.NUCLEAR REACTIONS ($p$,$t$), distorted-wave Born approximation analyses.

(Li7,t) on1f−2pshell nuclei

(/sup 7/Li,t) angular distributions have been measured on the targets /sup 40/Ca, /sup 44/Ca, and /sup 58/Ni at E=34 MeV for the ground and first excited state transitions. The results of the exact finite-range distorted-wave Born-approximation analyses of the data show a greater ..cap alpha.. spectroscopic strength for /sup 62/Zn than for either /sup 44/Ti or /sup 48/Ti.

C12(p,α*)B9reaction in the finite range microscopic distorted-wave Born-approximation formalism

The differential cross sections for the $^{12}\mathrm{C}$($p$,${\ensuremath{\alpha}}^{*}$)$^{9}\mathrm{B}$(g.s.) and $^{12}\mathrm{C}$($p$,$\ensuremath{\alpha}$)$^{9}\mathrm{B}$(g.s.) reactions were measured at forward angles at the proton energy of 45.2 MeV. The outgoing ${\ensuremath{\alpha}}^{*}$ particle (20.1 MeV, ${0}^{+}$, $T=0$) was detected by measuring in coincidence the proton and triton breakup products. Finite range distorted-wave Born approximation and final state interaction calculations were employed in describing the reaction with the unbound emitted particle. The form factor for the distorted-wave Born-approximation analysis was calculated in a microscopic model employing Woods-Saxon wave functions for the three individual transferred nucleons. Microscopic wave functions for the $\ensuremath{\alpha}$ and ${\ensuremath{\alpha}}^{*}$ particles, due to Hackenbroich et al., were used. Comparisons were also made with distorted-wave Born-approximation calculations using cluster transfer form factors. Relative normalizations between the ($p$,${\ensuremath{\alpha}}^{*}$) and the corresponding ($p$,$\ensuremath{\alpha}$) angular distribution were found to be in good agreement with theoretical prediction from the microscopic model.NUCLEAR REACTIONS $^{12}\mathrm{C}$($p$,${\ensuremath{\alpha}}^{*}$)$^{9}\mathrm{B}$, $^{12}\mathrm{C}$($p$,$\ensuremath{\alpha}$)$^{9}\mathrm{B}$, $E=45.2$ MeV; measured $\ensuremath{\sigma}({E}_{p},{E}_{t},\ensuremath{\theta})$, ${E}_{\mathrm{pt}}=0.285$ MeV, $\ensuremath{\sigma}({E}_{\ensuremath{\alpha}},\ensuremath{\theta})$; finite range DWBA analysis, microscopic and cluster form factors; final state interaction; relative normalization.

High-spin analog resonances near theN=50neutron shell

The $^{96}\mathrm{Zr}(^{3}\mathrm{He},d)^{97}\mathrm{Nb}$ and the $^{92}\mathrm{Mo}(^{3}\mathrm{He},d)^{93}\mathrm{Tc}$ reactions, investigated at, respectively, 39.0 and 28.5 MeV incident energies, were used to populate selectively high-spin analog resonances in $^{97}\mathrm{Nb}$ and $^{93}\mathrm{Tc}$. Angular distributions were measured for the ${d}_{\frac{3}{2}}$, ${g}_{\frac{7}{2}}$, and ${h}_{\frac{11}{2}}$ analog states of the low-lying levels in $^{97}\mathrm{Zr}$. A distorted-wave Born-approximation analysis of the data for these unbound levels (using Gamow functions as form factors) was carried out and spectroscopic strengths extracted. The $^{96}\mathrm{Zr}(^{3}\mathrm{He},dp)$ and $^{92}\mathrm{Mo}(^{3}\mathrm{He},dp)$ reactions were performed, respectively, at 37.5 and 30 MeV incident energies. The angular distributions of the emitted protons were measured in coincidence using method II of Litherland and Ferguson with 0\ifmmode^\circ\else\textdegree\fi{} detection of deuteron groups. Spins, population parameters, and proton branching ratios to the ground state and excited states of the targets were determined from the analysis of the angular correlation data. The position of the neutron threshold as compared with the excitation energies of the analog states in $^{97}\mathrm{Nb}$ and $^{93}\mathrm{Tc}$ is found to be an important parameter in the extraction of the structure information on core-excited components in the parent levels wave functions. Neutron particle-hole multiplets based on the $({d}_{\frac{5}{2}})_{n}^{}{}_{}{}^{\ensuremath{-}1}\ensuremath{\bigotimes}({h}_{\frac{11}{2}})_{n}^{}{}_{}{}^{+1}$ and $({d}_{\frac{5}{2}})_{n}^{}{}_{}{}^{\ensuremath{-}1}\ensuremath{\bigotimes}({g}_{\frac{7}{2}})_{n}^{}{}_{}{}^{+1}$ configurations are observed for the first time in $^{96}\mathrm{Zr}$ through the decay of the ${g}_{\frac{7}{2}}$ and ${h}_{\frac{11}{2}}$ analog resonances. The limitation of the present method due to the neutron threshold or to the energy resolution in the proton channel is discussed and compared with the results of inelastic resonant scattering through isobaric analog resonances.NUCLEAR REACTIONS $^{92}\mathrm{Mo}(^{3}\mathrm{He},d)$ $E=28.5$ MeV; measured $\ensuremath{\sigma}({E}_{d},\ensuremath{\theta})$, $\ensuremath{\theta}=20\ifmmode^\circ\else\textdegree\fi{},35\ifmmode^\circ\else\textdegree\fi{}$. $^{96}\mathrm{Zr}(^{3}\mathrm{He},d)$ $E=39.0$ MeV; measured $\ensuremath{\sigma}({E}_{d},\ensuremath{\theta})$. $^{92}\mathrm{Mo}(^{3}\mathrm{He},d\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{p})$ $E=30$ MeV, $^{96}\mathrm{Zr}(^{3}\mathrm{He},d\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{p})$ $E=37.5$ MeV; measured $\ensuremath{\sigma}({E}_{d},{E}_{p},{\ensuremath{\theta}}_{P})$. $^{93}\mathrm{Tc}$, $^{97}\mathrm{Nb}$ deduced IAS, $L$, $J$, $\ensuremath{\pi}$, $S$, ${\ensuremath{\Gamma}}_{p}$, ${\ensuremath{\Gamma}}_{{p}^{\ensuremath{'}}}$. DWBA analysis using Gamow functions as form factors. Magnetic analysis. Enriched targets.

Hole states excited by theMg24(p,d)Mg23reaction at 95 MeV

Experimental excitation energies and angular distributions have been obtained for 33 deuteron groups from the $^{24}\mathrm{Mg}$($p$,$d$) reaction at 94.8-MeV bombarding energy with 80-keV experimental resolution. Energies obtained for states in $^{23}\mathrm{Mg}$ are in agreement with the sixth compilation of Endt and van der Leun up to 7.25 MeV and the recent unpublished ($p$,$t$) study of Nann et al. up to 9.72 MeV. Energies are determined in the present work for 18 additional groups corresponding to excitations between 9.8 and 13.28 MeV. Angular distributions from 6\ifmmode^\circ\else\textdegree\fi{} to 88\ifmmode^\circ\else\textdegree\fi{} laboratory (momentum transfers up to 660 MeV/c) show characteristic oscillatory signatures for $l=0$ transitions and broad peaked nonoscillatory behavior for presumed multistep transitions. $l=1 \mathrm{and} 2$ transitions show a very similar exponential falloff with large momentum transfer, but they can be clearly distinguished by their small-angle behavior after division by an empirical exponential factor or by the dominant momentum transfer dependence from a plane-wave analysis. $l=1$ transitions are observed to deep-hole states at 8.91-, 9.02-, 9.67-, and 10.57-MeV excitation. The angular distributions also lead to very probable assignments of $\frac{5}{{2}^{\ensuremath{-}}}$ and $\frac{7}{{2}^{+}}$ to the 3.97- and 4.68-MeV states of $^{23}\mathrm{Mg}$, and are consistent with $\frac{9}{{2}^{+}}$ and $\frac{11}{{2}^{+}}$ assignments to the 2.71- and 5.45-MeV states. Distorted-wave Born approximation (DWBA) predictions using optical potentials from published elastic scattering results show rather good agreement with the shapes of the observed angular distributions for $l=2$ transitions, but spectroscopic factors vary by up to a factor of 3 depending on the deuteron potential employed. $l=0$ transitions are not fitted in either shape or position of the oscillations, which may be due to the fact that deuteron wave functions derived from elastic scattering are not accurate in the nuclear interior. Reasonable shapes are predicted by preliminary coupled-channel Born approximation (CCBA) analyses for transitions believed to proceed in two steps.NUCLEAR REACTIONS $^{24}\mathrm{Mg}$ ($p$,$d$), $E=94.8$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$. $^{23}\mathrm{Mg}$ levels deduced $l$, $J$, $\ensuremath{\pi}$. $S$. DWBA analysis, resolution 80 keV, $\ensuremath{\theta}=6\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}88\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=2\ifmmode^\circ\else\textdegree\fi{} or 4\ifmmode^\circ\else\textdegree\fi{}$, ${E}_{x}=0\ensuremath{-}13.28$ MeV.

Calculation of theS- andD-state components of the deuteron-triton overlap integral

The $S$- and $D$-state components of the deuteron-triton overlap integral and of the form factor required for a distorted-wave Born-approximation analysis of ($d$,$t$) reactions have been calculated for a number of variational triton wave functions corresponding to realistic nucleon-nucleon potentials. It is found that the calculated overlap functions decay too rapidly for large $n\ensuremath{-}d$ separations, and this has important consequences for the corresponding distorted-wave Born-approximation form factors. In particular, the parameter ${D}_{2}$, which measures the relative importance of the $D$-state form factor in the low-momentum limit, is found to be more than a factor of 2 smaller than the best experimental value. A more direct calculation of the form factors leads to a much larger value of ${D}_{2}$.NUCLEAR REACTIONS DWBA theory; calculated deuteron-triton overlap and form factors for ($d$,$t$) reactions.

Neutron pickup fromS33

At a bombarding energy of 15 MeV, angular distributions have been measured for the /sup 33/S(/sup 3/He,..cap alpha..) reaction leading to 25 levels of /sup 32/S below 8 MeV excitation. A distorted-wave Born-approximation analysis has provided l values and relative spectroscopic factors for most of these. Results are in moderate agreement with shell-model calculations, but exhibit less configuration mixing than is predicted.

The α-transfer reactions 27Al( 6Li, d) 31P, 29Si( 6Li, d) 33S and 31P( 6Li, d) 35Cl at 36 MeV

The α-transfer reactions 27Al( 6Li, d) 31P, 29Si( 6Li, d) 33S and 31P( 6Li, d) 35Cl have been studied at a 6Li energy of 36 MeV. Absolute cross sections and angular distributions have been measured and an exact finite-range distorted-wave Born approximation analysis assuming a direct cluster transfer has been used to extract from the data α-particle spectroscopic strengths for levels populated in 31P, 33S and 35Cl in the three reactions respectively. The results show that in the case of most of the low-lying excited states of 31P, a single value of L of the transferred α-particle contributes, though a multiplicity of L-values are allowed by angular momentum selection rules. It is also found that the α-particle spectroscopic strength of the ground state of 31P is a factor of 2 more than the strengths of the ground states of 33S and 35Cl. The α-spectroscopic strengths of ground states of these, as well as other odd- A s-d shell nuclei, are compared with the presently available shell model calculations.

Nuclear structure ofTc94

Levels in $^{94}\mathrm{Tc}$ up to an excitation of 4.5 MeV were populated by means of the $^{92}\mathrm{Mo}$($^{3}\mathrm{He}$,$p$)$^{94}\mathrm{Tc}$ reaction at ${E}_{^{3}\mathrm{He}}=25$ MeV. Distorted-wave Born-approximation analyses of the proton angular distributions lead to spin and parity assignments for several levels. Coupled channel calculations predict that contributions of a sequential ($p\ensuremath{-}n$) transfer mechanism are important and angular distributions for the lowest ${0}^{+}$, ${1}^{+}$, and ${2}^{+}$ states are better accounted for by interference effects between one- and two-step processes. A possible ${0}^{+}$ state at 2.72 MeV excitation is suggested to be the [${{d}_{\frac{5}{2}}}^{p}{{d}_{\frac{5}{2}}}^{n}$] antianalog of the $^{94}\mathrm{Mo}$ ground state.NUCLEAR REACTIONS $^{92}\mathrm{Mo}$ ($^{3}\mathrm{He}$, $p$), $E=25$ MeV; measured $\ensuremath{\sigma}(Ep, \ensuremath{\theta})$, $\ensuremath{\theta}=5\ifmmode^\circ\else\textdegree\fi{}\ensuremath{-}50\ifmmode^\circ\else\textdegree\fi{}$, $\ensuremath{\Delta}\ensuremath{\theta}=5\ifmmode^\circ\else\textdegree\fi{}$, enriched target, split-pole spectrograph. $^{94}\mathrm{Tc}$ deduced levels, ${L}_{\mathrm{np}}$, ${J}^{\ensuremath{\pi}}$. DWBA and CRC analyses.

αclustering inPb208from (d,Li6) atEd=55MeV

The reaction $^{208}\mathrm{Pb}$($d$,$^{6}\mathrm{Li}$)$^{204}\mathrm{Hg}$ has been observed at ${E}_{d}=55$ MeV. Data for several levels in $^{204}\mathrm{Hg}$ up to ${E}_{x}\ensuremath{\simeq}3.5$ MeV have been obtained and alpha-particle spectroscopic factors and reduced alpha widths for $^{208}\mathrm{Pb}$ deduced with distorted-wave Born approximation analyses. The reduced alpha widths have been utilized to deduce the "alpha decay" properties of $^{208}\mathrm{Pb}$, as well as superheavy nuclei. The analysis indicates $log{{T}^{\ensuremath{\alpha}}}_{\frac{1}{2}}(\mathrm{years})=127.4\ifmmode\pm\else\textpm\fi{}1.0$ for $^{208}\mathrm{Pb}$ and $log{{T}^{\ensuremath{\alpha}}}_{\frac{1}{2}}(\mathrm{years})=2.5\ifmmode\pm\else\textpm\fi{}2.0$ for $Z=114$, $N=184$ and ${Q}_{\ensuremath{\alpha}}=7.0\ifmmode\pm\else\textpm\fi{}0.5$ MeV. The results also imply that about 1% of the protons in $^{208}\mathrm{Pb}$ at $r=10$ fm are associated with alpha clusters.NUCLEAR REACTIONS $^{108}\mathrm{Pb}$($d$,$^{6}\mathrm{Li}$) $^{204}\mathrm{Hg}$, $E=54.8$ MeV; measured $\ensuremath{\sigma}(\ensuremath{\theta})$. $^{204}\mathrm{Hg}$ deduced levels, ${S}_{\ensuremath{\alpha}}$, ${\ensuremath{\gamma}}_{\ensuremath{\alpha}}^{2}(10 \mathrm{fm})$. DWBA analyses. Magnetic spectrometer.

Effects of Spin-Orbit Deformation in Inelastic Scattering at 0.8 GeV

New differential cross section and analyzing-power data for 800-MeV p/sub pol/ + /sup 12/C, /sup 116,124/Sn inelastic scattering to the first 2/sup +/ states are presented. A distorted-wave Born-approximation analysis which utilizes collective form factors and includes deformation of the spin-orbit potential is shown to provide a reasonable description of the analyzing-power data.

Comparison of theSi28(O16,C12)S32andSi28(O18,C14)S32reactions at

Cross-section angular distributions of the $^{28}\mathrm{Si}$($^{16}\mathrm{O}$, $^{12}\mathrm{C}$)$^{32}\mathrm{S}$ and the $^{28}\mathrm{Si}$($^{18}\mathrm{O}$, $^{14}\mathrm{C}$)$^{32}\mathrm{S}$ reactions leading to lowlying states in $^{32}\mathrm{S}$ and the $^{18}\mathrm{O}$+$^{28}\mathrm{Si}$ elastic scattering have been measured at 60 MeV incident energy. Optical model parameters were obtained by the analysis of the measured $^{18}\mathrm{O}$+$^{28}\mathrm{Si}$ elastic scattering and the analysis of existing $^{16}\mathrm{O}$+$^{28}\mathrm{Si}$ elastic scattering data. The exact finite-range distorted-wave Born approximation analysis of the ($^{16}\mathrm{O}$, $^{12}\mathrm{C}$) reaction data showed that the transfer data could only be reproduced using a surface-transparent set of optical model parameters. On the contrary no optical model parameters could be found which provide simultaneously good fits of the $^{18}\mathrm{O}$+$^{28}\mathrm{Si}$ elastic scattering and the ($^{18}\mathrm{O}$, $^{14}\mathrm{C}$) transfer data. The transfer data could be reproduced however, using optical model parameters which do not describe elastic scattering data. Relative spectroscopic factors were extracted for both transfer reactions and are compared with previous results of ($^{16}\mathrm{O}$, $^{12}\mathrm{O}$) and ($^{6}\mathrm{Li}$,$d$) reaction studies. In addition we determined spectroscopic factors of the $^{28}\mathrm{Si}$($^{12}\mathrm{C}$, $^{8}\mathrm{Be}$) $^{32}\mathrm{S}$ reaction by reanalyzing existing data. The comparision suggests the conclusion that the ($^{16}\mathrm{O}$, $^{12}\mathrm{C}$) and ($^{18}\mathrm{O}$, $^{14}\mathrm{C}$) reactions proceed through different reaction mechanisms.

N+dclustering of three-nucleon systems:D-state effects in (d,t) andd,He3) reactions

The $S$- and $D$-state radial components ${u}_{0}$ and ${u}_{2}$ of the relative motion between the clusters $d+n$ in $^{3}\mathrm{H}$ necessary in a full finite range distorted-wave Born-approximation analysis of ($d$,$t$) reactions, are calculated using realistic triton and deuteron wave functions derived from the Reid soft-core potential. The parameter ${D}_{2}$ which provides a measure of the asymptotic $D$ state to $S$ state ratio is found to be almost entirely determined by the triton $D$ state, the deuteron $D$-state contribution being about 10%. Using the Strayer and Sauer triton wave function, the value ${D}_{2}=\ensuremath{-}0.17$ ${\mathrm{fm}}^{2}$ is obtained after correcting the asymptotic behavior of the $d\ensuremath{-}t$ overlap. This result suggests that the Reid soft-core potential overestimates ${D}_{2}$ by about 20% compared with values extracted from a local energy approximation analysis of ($d$,$t$) tensor analyzing power data. The difference between ${D}_{2}$ for ($d$,$t$) and ($d$,$^{3}\mathrm{He}$) is discussed.NUCLEAR STRUCTURE $^{3}\mathrm{H}$; calculated $S$ and $D$ states of the overlap integral with deuteron; deduced ${D}_{0}$ and ${D}_{2}$ for ($d$,$t$) and ($d$, $^{3}\mathrm{He}$) reactions.

Inner hole states inPb207via thePb208(He3, α)Pb207reaction at 70 MeV

The $^{208}\mathrm{Pb}(^{3}\mathrm{He}, \ensuremath{\alpha})^{207}\mathrm{Pb}$ reaction at 70 MeV incident energy was used to populate hole states up to 28 MeV excitation energy in $^{207}\mathrm{Pb}$. A split-pole spectrometer was used for particle analysis and detection. For the excitation energy range between 0 to 4.5 MeV, about eleven well resolved states are excited. These levels contain the main part of the spectroscopic strengths of the $3{p}_{\frac{1}{2}}$, $2{f}_{\frac{5}{2}}$, $3{p}_{\frac{3}{2}}$, $2{f}_{\frac{7}{2}}$, $1{i}_{\frac{13}{2}}$, and $1{h}_{\frac{9}{2}}$ neutron subshells. Three additional regions of enhanced cross sections, centered at 5.5, 8.5, and 14 MeV excitation energy in $^{207}\mathrm{Pb}$, are also observed. The 65 keV energy resolution of the present study revealed fine structure in the peak previously observed around 8.5 MeV in $^{207}\mathrm{Pb}$. About fifteen levels or groups of levels are populated between 4.5 and 10.5 MeV, and angular distributions have been extracted for each individual peak as well as for the gross structures. A distorted-wave Born-approximation analysis of the data was carried out and shows that the missing $l=3 \mathrm{and} 5$ strengths in $^{207}\mathrm{Pb}$ are located in some strong peaks at 5.13, 5.62, and 6.37 MeV. Thus the full sum rule is obtained for the neutron subshells between $N=126$ and $N=82$. The highly fragmented peak located at 8.5 MeV excitation energy is shown to arise from $1{h}_{\frac{11}{2}}$ neutron pickup. Finally, the large structure, 5 MeV wide and centered around 14 MeV, observed for the first time in this work is tentatively interpreted as arising from neutron pickup from the $1{g}_{\frac{9}{2}}$ inner shell. The ${T}_{>}$ components of the deeply-bound state are also observed between 20 to 24 MeV in $^{207}\mathrm{Pb}$ and therefore from the sum-rule analysis, centroid energies and total strengths for each inner subshell are deduced.NUCLEAR REACTION $^{208}\mathrm{Pb}(^{3}\mathrm{He}, \ensuremath{\alpha})$, $E=70$ MeV; measured $\ensuremath{\sigma}(E, \ensuremath{\theta})$. $^{207}\mathrm{Pb}$ deduced levels, ${E}_{x}$, $l$, ($J$), $\ensuremath{\pi}$, ${C}^{2}S$; inner shell spectroscopic factors; enriched target, magnetic spectrometer.

Slowly converging integrals in the analysis of deuteron stripping to decaying states

The slowly converging overlap integral appearing in the distorted wave Born approximation analysis of deuteron stripping to decaying states is treated by employing a Gaussian convergence factor to ensure proper convergence. Numerical results are presented and the usefulness of the above technique in handling stripping overlap integrals in the continuum region is discussed.NUCLEAR REACTIONS $^{32}\mathrm{S}(d, p)$ reactions, unbound state, calculated $\ensuremath{\sigma}({E}_{p}, {\ensuremath{\theta}}_{p})$, ${E}_{D}=12.0$ MeV, method of handling the divergent integrals discussed.

Structure ofGe78from theGe76(t, p)Ge78reaction

The /sup 76/Ge(t,p)/sup 78/Ge reaction has been performed at a bombarding energy of 17 MeV. Thirteen excited states below 3 MeV excitation are reported with J/sup ..pi../ values obtained by comparison to distorted-wave Born-approximation analysis. A comparison to a dynamical deformation theory is made and the results suggest /sup 78/Ge is a transitional nucleus nearing spherical shape due to the proximity of the N = 50 closed shell.

Proton Inelastic Scattering on 28,29,30Si and Blocking Effect in the Core-Excitation of 29Si

Angular distributions of elastic and inelastic scatterings on 28,29,30 Si were measured with a 51.9 MeV proton beam. The blocking effect in the core-excitation of 29 Si due to the antisymmetrization between the excited-core and the extra neutron was investigated. Optical model and distorted wave Born approximation analyses were performed using a macroscopic form factor for a collective excitation of 28,29,30 Si and a microscopic form factor for a single particle excitation of 29 Si. In the case of 29 Si, a mixing of an excited-core state and a single particle state was taken into account following the intermediate-coupling model calculation. Deformation parameters β 2 of 28,29,30 Si were extracted to be 0.42, 0.36 and 0.36, respectively. The reduction in the deformation parameter of 29 Si is considered to manifest the blocking effect of 25±14% in the core-excitation.