The ground-state energy of nuclear matter is expanded in such a way that each term of the expansion is characterized by the number of hole lines. This procedure reverses the usual sequence of steps, which consists in the use of the linked-cluster theorem, the introduction of $G$ matrices, and the partial summation of $G$-matrix diagrams leading to the hole-line expansion. In this way, we find an algebraic method which yields automatically all diagrams with a fixed number of independent hole lines. As a by-product, a new proof for the linked-cluster theorem is obtained. We have applied the method to diagrams with four independent hole lines and find complete agreement with results published previously by B. D. Day.

Precision excitation energies of 16 levels in ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ measured with the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ reaction are reported. The values based on an assumed excitation energy for the fourth excitated state of 5105.87 keV are 3950.2, 4915.3, 5688.8, 5832.4, 6202.5, 6444.9, 7027.9, 7964.9, 8486.4, (8617.4), 8909.9, 8959.8, (8977.3), 9124.1, 9167.4, and 9385.4 keV. Random uncertainties range from 1.4 to 1.9 keV. The width of the 8909.9-keV level was measured as 19.7 ± 1.9 keV and that of the 9385.4-keV level as 15.6±2.0 keV. Angular distributions measured at 11.95 MeV are given for these 16 levels and for the 5106-keV level. The states at 2312, 8063, and 8710 keV were not measured.

Marumori's boson-expansion method is applied to the problem of particle-hole excitation in closed-shell nuclei. It is shown that consistent (and in principle, straightforward) calculations yield correct results for the ground-state correlation energy, occupation probabilities, and the lowest-order random-phase approximation. A method introducing higher-order random-phase approximations based on the tranformation of Rowe's formulation in particle-hole space is described.

We investigate the contribution of three-body forces to the binding energy of nuclear matter, including the effects of two- and three-body correlations induced by the two-nucleon forces, and find that it may by approximated using plane-wave three-nucleon states cut off when any interparticle distance is less than about 0.9 fm. Existing calculations can then be used to estimate that three-body forces contribute about 1 MeV to the binding energy.

We have measured the neutron-proton total cross section in hydrogen gas at 0°C between 0.3- and 400-eV lab energy to help improve the data for computing the $n-p$ singlet effective range $r_s$. To obtain the free $n-p$ scattering cross section at "zero" energy, we subtract the capture-cross-section, effective-range, and molecular-binding contributions from the total cross section. We used the asymptotic "MTV" theory of molecular binding due to Messiah, which limits our final analysis to the range 6.02 to 329 eV. From these data we obtain 20.436 ± 0.023 b for the free $n-p$ scattering cross section. Using this number, the coherent-scattering-length measurements by Koester, a model due to Lomon and Feshbach for the triplet and singlet shape parameters, and the $n-p$ cross section in the MeV range due to Engelke et al., we obtain $r_s=2.56\mathrm{}\pm 0.05$ F, 0.09 F higher than the former value. Adopting an energy scale due to Davis and Barschall for the higher-energy data raises $r_s$ to 2.74 F, which is in close agreement with the value 2.70 F predicted by the charge-independence hypothesis. A measurement of the neutron-carbon cross section, formerly related to this problem, is also discussed.

The polarization of the neutrons from the ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}\mathrm{}(p,n)\mathrm{}$ reaction leading to the first three levels of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ has been measured at six bombarding energies between 7.2 and 13.3 MeV. The polarization and angular distribution of the neutrons leading to the two $1^{+}$ states have been analyzed with a microscopic distorted-wave Born-approximation formalism that has been extended to include spin-orbin optical distortions and a tensor component in the effective two-body force; the analog-state transition has been analyzed with the Lane model. The angular distribution and polarization shapes for the analog transition are not well reproduced by the Lane model, primarily because of lack of precise optical parameters as a function of bombarding energy. However, the integrated cross sections between 8.8 and 18.3 MeV are reasonably well accounted for with a constant real and imaginary isospin strength of 88 and 40 MeV, respectively. The corresponding real microscopic charge-exchange strength is $V_{\tau }=9\mathrm{}$ MeV for a Yukawa form factor of range 1.4 fm. The calculated $1^{+}$ angular-distribution shapes are in fair agreement with measurements and are consistent with a constant central spin-spin and tensor strength between 10.4- and 18.3-MeV bombarding energy: $V_{\sigma \tau }=7\mathrm{}\pm 1$ MeV and $V_T=4.7\mathrm{}\pm 0.7$ MeV, although there is some indication that the tensor strength is decreasing with increasing energy. Contrary to the angular-distribution measurements, the $1^{+}$ polarization measurements do not clearly favor a tensor component in the effective two-body force; neither the pure central nor the central-plus-tensor polarization calculation fits the data particularly well. This disagreement is probably due to optical-parameter uncertainities and contributions from second-order processes, and possibly to the neglect of tensor exchange and small admixtures of intermediate-structure resonance processes.

Semileptonic interactions with anomalous, i.e., "second-class," $G$-parity properties are uniquely correlated with certain characteristic terms in the amplitude for $\beta$ decay between members of a common isotopic multiplet. The observational effects associated with second-class currents are worked out for several features of the $\beta$-decay spectrum as well as for $\beta -\gamma$ correlation phenomena.

The two-nucleon pion-absorption operator of Koltun and Reitan is applied to the pionic dis-integration process of ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. The target nucleus is represented by the cluster-model wave function of Tang, Wildermuth, and Pearlstein. The pion-absorption operator is of nonzero-range character and takes into account both the direct-absorption and the rescattering processes. The transition probability of the decay turns out to depend on the two parameters associated, respectively, with the intercluster distance and the size of the deuteron in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$. The values of these two parameters are determined so as to fit the experimental momentum distribution of the two final neutrons to within experimental error. The possibility of the existence of a second peak in the momentum distribution is also discussed.

The contribution of two-particle-two-hole excitations to the Hartree-Fock energy in the ground state of ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ favors an axially symmetric prolate shape over the nonaxial shape preferred on the basis of bare Hartree-Fock calculations. The second-order contribution, however, does not affect the prediction of Hartree-Fock calculations of ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$.

The mean lifetimes of 15 excited states of ${\mathrm{Sc}}^{43}$ and upper and/or lower bounds for six others have been measured by the Doppler-shift attenuation method. The ${\mathrm{Ca}}^{40}(\alpha ,p\gamma )$ and ${\mathrm{Ca}}^{42}-(p,\gamma )$ reactions were used to populate the levels. For the ($\alpha ,p\gamma$) measurements, $\gamma$ rays were detected at 90° to the $\alpha$-particle beam in coincidence with protons detected at + 110 and -110°. The ${\mathrm{Sc}}^{43}$ ions were stopped in thick carbon backings, the stopping power of which is known from previous experimental work. For the ($p,\gamma$) measurements, $\gamma$ rays were detected at 0 and 135° to the proton beam. The ${\mathrm{Sc}}^{43}$ ions were stopped in the target material. The results yield the following mean lives, in fsec (with the level energies in MeV given in parentheses): 230 ± 70 (0.846), >620 (0.856), 800 ± 300 (0.880), ${3100}_{-1200\mathrm{}}^{+2700\mathrm{}}\mathrm{}\left(1.158\right)\mathrm{}$, 400 ± 190 (1.179), 850 ± 250 (1.336), 240 ± 50 (1.410), 330 ± 100 (1.651), 22 ± 7 (1.810), 300 ± 50 (1.827), 80 ± 50 (1.885), >800 (1.930), 100 ± 20 (1.963), 410 ± 150 (2.094), 260 ± 70 (2.143), 150 ± 50 (2,580), 80 ± 20 (2.986), <5 (3.289), <10 (3.452), <5 (3.807), and <5 (4.455). The lifetime results for the 1.158- and 1.652-MeV levels are used to remove ambiguities in the measured mixing ratios. All results are compared with theoretical predictions of Johnstone and co-workers.

A study of the dipole spectrum of analog states in ${\mathrm{Y}}^{89}$ is presented. Both ground-state decays and transitions to the second excited ${\frac{3}{2}}^{-}$ state are discussed. The angular momentum and parity quantum numbers of the levels under consideration are ${\frac{1}{2}}^{+}$, ${\frac{3}{2}}^{+}$, and ${\frac{5}{2}}^{+}$. As in previous work in even-even nuclei, most of the radiative strength is found concentrated in the high-energy region of the spectrum.

Yields of several radionuclides in thin iron targets were measured for electron bombarding energies of 40-MeV to 16-GeV. In general the yields appear to approach zero at bombarding energies near threshold energies for nuclide production by nucleon emmission from the target nucleus. The effect of bombarding energy on the yield surface for cascade-evaporation reactions was investigated by comparing ratios of yields; the results suggest that except for the slope of the ridge the shape of the yield surface does not vary with energy for bombarding energies above a few hundred MeV.

${\mathrm{Na}}^{25}$ was produced in the ${\mathrm{Na}}^{23}\mathrm{}(t,p)\mathrm{}{\mathrm{Na}}^{25}$ reaction and its radiations were investigated by means of Ge(Li), plastic, and NaI(Tl) detectors. From $\beta -\gamma$ coincidence experiments the ${\mathrm{Na}}^{25}$ $\beta$-ray branch to the ground state of ${\mathrm{Mg}}^{25}$ is 62.5±2.0%. Other $\beta -$ and $\gamma$-ray branches were derived from the $\gamma$-ray spectrum and are in agreement with previous results. From both singles and $\gamma -\gamma$ coincidence measurements a limit of <0.02% ($log\mathrm{ft}>\mathrm{}6.5\mathrm{}$) is placed on the $\beta$-ray branch to the 2738-keV $J^{\pi }={\frac{7}{2}}^{+}$ state of ${\mathrm{Mg}}^{25}$. Recent shell-model calculations give a good account of the relative experimental $\beta$-branching intensities and, in particular, predict that the transition to the 2738-keV state should be very weak.

The broken-pair approximation (BPA), introduced as a number-conserving approximation to the lowest-seniority shell model (LSSM), is applied to the nickel and tin isotopes. The shell-model interactions used are microscopically derived from the Tabakin potential and the Yale-Shakin reaction matrix or phenomenologically determined (by the Argonne group) through a shell-model-fit procedure. The results are compared with those of standard quasiparticle calculations (QTD) and, when possible, of the exact shell model (ESM) and of the LSSM. It is found that the BPA and the QTD can give essentially different results. Comparison with the LSSM and the ESM indicates that the BPA is a much more reliable approximation than the QTD.

The mean lives of the 2312-, 3947-, and 6203-keV levels of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ have been measured with the Doppler-shift-attenuation (DSA) method through the reaction ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(p,\gamma ){}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ ($E_p=1.15\mathrm{}$ MeV) using C, Ti, Ag, Mo, Ni, Ta, Au, and W as stopping materials. ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ ions were separated both onto and into the backings. The results show in this case about ±20% anomalies. Some sources of error arising from target preparation are discussed. In DSA measurements of short lifetime the use of implanted targets seems to be advantageous. The measured lifetimes are given as 70 ± 10, 10.5 ± 3.5, and 118 ± 13 fsec, respectively.

The energy levels of ${\mathrm{Cl}}^{34}$ have been studied with the ${\mathrm{S}}^{33}({\mathrm{He}}^3,d){\mathrm{Cl}}^{34}$ reaction induced by the 14-MeV ${\mathrm{He}}^3$ beam of the Argonne tandem Van de Graaff accelerator. An Enge split-pole magnetic spectrograph was used to record the deuteron spectra at scattering angles of 10-65° in 5° steps. An over-all energy resolution width of 17 keV was achieved. 26 levels up to an excitation energy of 4.6 MeV were observed and their spectroscopic factors were extracted. The results, when combined with previously known spin information, enable us to locate the major components of ${\left(d_{\frac{3}{2}}\right)}^2$ and $d_{\frac{3}{2}}{f}_{\frac{7}{2}}$ configurations. The two-body matrix elements obtained here are compared with other two-body data in nearby nuclei and with calculated matrix elements.

About 50 levels of ${\mathrm{V}}^{50}$ below 3.2 MeV have been studied with 9- to 15-keV resolution via the ${\mathrm{V}}^{51}\mathrm{}(d,t)\mathrm{}{\mathrm{V}}^{50}$, ${\mathrm{Cr}}^{52}(d,\alpha ){\mathrm{V}}^{50}$, and ${\mathrm{Ti}}^{48}({\mathrm{He}}^3,p){\mathrm{V}}^{50}$ reactions. Angular distributions were taken (at 16 MeV) for the ${\mathrm{V}}^{51}\mathrm{}(d,t)\mathrm{}$ reactions and (at 17 MeV) for ${\mathrm{Cr}}^{52}(d,\alpha ){\mathrm{V}}^{50}$. ($d,t$) and ($d,\alpha$) $l$ values were extracted by comparison with distorted-wave Born-approximation calculations. For most of the levels seen, direct-reaction selection rules lead to narrow limits for the final-state spins, and in a few cases to unique $J^{\pi }$ assignments. The spectroscopic information for the lowest levels was compared with shell-model predictions, and qualitative agreement was found. The lowest negative-parity states seen were above 2 MeV. Little $2p$ strength was found in the pickup experiments, and strong suppression of ($d,\alpha$) transitions to $J^{\pi }={\left(\mathrm{even}\right)}^{+}$ states suggests that the low-lying states of ${\mathrm{V}}^{50}$ are predominantly of ${\left(f_{\frac{7}{2}}\right)}^n$ configuration. However, a comparison with the ($d,\alpha$) spectrum for the particle-hole conjugate nucleus ${\mathrm{Sc}}^{46}$ shows that these nuclei are more dissimilar than a simple ${\left(f_{\frac{7}{2}}\right)}^n$ model would suggest.

The radiative widths of the $E1\mathrm{}$ transition through the ground isobaric analog states of ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ in ${}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}$ and ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, respectively, were determined from the cross section of the ($e,e^{\prime }p$) reaction. The results are 98 and 140 eV, respectively, after the correction for the interference from the continuous part of the reaction. They correspond to an effective charge of 0.56 and 21, respectively. The $E1\mathrm{}$ matrix elements were determined and used for the estimation of $\beta$ matrix elements $|i\xi ``\int \overrightarrow{\mathrm{r}}\text{'}\text{'}|$. The result is 0.055 in natural units ($\hslash =c=m_e=1\mathrm{}$) for the $\beta$-decay ${}_{}{}^{207}{}_{}{}^{}\mathrm{Tl}\left(3\mathrm{}{s_{\frac{1}{2}}}^{-1\mathrm{}}\right)\to {}_{}{}^{207}{}_{}{}^{}\mathrm{Pb}\left(3\mathrm{}{p_{\frac{1}{2}}}^{-1\mathrm{}}\right)$. In the case of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}\left(2\mathrm{}{g}_{\frac{9}{2}}\right)\to {}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}\left(1\mathrm{}{h}_{\frac{9}{2}}\right)$, the result is 0.043, which is much larger than the theoretical estimate. For the $E1\mathrm{}$ isobaric analog states of the first excited state of ${}_{}{}^{209}{}_{}{}^{}\mathrm{Pb}$ in ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$, the radiative width and the effective charge were also determined to be 170 eV and 0.46, respectively.

The ratio $\left|\frac{M^{\beta }}{\xi i\int \overrightarrow{\mathrm{r}}}\right|$ for the first-forbidden ${\beta }^{-}$ decay has been studied to discuss the composition of $M^{\beta }$. Experimental values of $\left|M^{\beta }\right|$ and $\left|i\int \overrightarrow{\mathrm{r}}\right|$ are estimated from $\mathrm{ft}$ values and from the $E1\mathrm{}$ matrix element. The latter was obtained from the ($e,e^{\prime }p$) reaction through the isobaric analog states in ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$, ${}_{}{}^{141}{}_{}{}^{}\mathrm{Pr}$, and ${}_{}{}^{148}{}_{}{}^{}\mathrm{Sm}$. The experimental value of the ratio was compared with the theory using a $j-j$-coupling shell model. The result shows good agreement for ${}_{}{}^{141}{}_{}{}^{}\mathrm{Ce}$ but not always good agreement for ${}_{}{}^{139}{}_{}{}^{}\mathrm{Ba}$ and ${}_{}{}^{148}{}_{}{}^{}\mathrm{Pm}$.

The internal-conversion coefficient of the 223-keV transition was determined, from precise $\gamma$-ray and conversion intensities, as ${\alpha }_K\mathrm{}\left(223\right)=0.082\mathrm{}\pm 0.004$. $\gamma -\gamma$ directional correlations of the ${\gamma }_{223}-{\gamma }_{80+81}$ and ${\gamma }_{276}-{\gamma }_{80+81}$ cascades were measured using a 33-${\mathrm{cm}}^3$ Ge(Li) detector and a 2 × 2-in. NaI(Tl) detector. The $A_{22}$ coefficients are $A_{22}({\gamma }_{276}-{\gamma }_{80+81})=+0.100\mathrm{}\pm 0.004$ and $A_{22}({\gamma }_{223}-{\gamma }_{80+81})=-0.030\mathrm{}\pm 0.004$, which are consistent with $\delta \mathrm{}\left(223\right)=-0.108\mathrm{}\pm 0.014$. These values of ${\alpha }_K$ and $\delta$ imply $\lambda \mathrm{}\left(223\right)=2_{-3\mathrm{}}^{+4\mathrm{}}$, consistent with a normal conversion process for this transition. In addition, the relative correlations of the $K_{276}-{\gamma }_{161}$ and $K_{276}-{\gamma }_{80+81}$ cascades were measured using a magnetic-lens spectrometer and 2 × 2-in. NaI(Tl) detector. The ratio of these $A_{22}$ coefficients allows cancellation of electron scattering factors, spectrometer geometry factors, and correlation attenuation factors. The results imply $\delta \mathrm{}\left(161\right)=+{0.59}_{-0.16\mathrm{}}^{+0.18\mathrm{}}$, which supports the existence of large penetration effects in the 161-keV transition.