Angular correlations of $\gamma$ rays deexciting states in ${}_{}{}^{38}{}_{}{}^{}\mathrm{K}$ have been measured. The reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(d,\alpha \gamma ){}_{}{}^{38}{}_{}{}^{}\mathrm{K}$ ($E_d=4.421\mathrm{} \mathrm{and} 5.080$ MeV), with ${\theta }_{\alpha }$ near 180° was used to populate levels of ${}_{}{}^{38}{}_{}{}^{}\mathrm{K}$. The decay of levels below an excitation energy of 3.7 MeV is given. Unique spin-parity assignments of $1^{+}$, $1^{+}$, and $2^{+}$ could be made for the second, third, and fourth excited states. In addition, limitations could be imposed on spins and parities of seven other excited states. Multipole mixing ratios of the decay $\gamma$ rays are given. Yield measurements, averaged over a large incident deuteron energy range, provided information on spin-parity assignments of two excited states.

The residual activity between bursts of a mechanically chopped beam has been used to measure the yield of the reaction ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(p,\gamma ){}_{}{}^{33}{}_{}{}^{}\mathrm{Cl}$ systematically in the bombarding energy range $E_p=3.36\mathrm{} \mathrm{to} 5.41$ MeV. Two $T=\frac{3}{2}$ states in ${}_{}{}^{33}{}_{}{}^{}\mathrm{Cl}$ at $E_p=3.371\mathrm{}\pm 0.005$ MeV, $E_x=5.550\mathrm{}\pm .007$ MeV and at $E_p=5.282\mathrm{}\pm .006$ MeV, $E_x=7.402\mathrm{}\pm .008$ MeV have been located with the resonance strengths $\frac{\mathrm{}(2J+1)\mathrm{}{\Gamma }_{p_0}{\Gamma }_{\gamma }}{\Gamma }=0.76\mathrm{}\pm 0.18 \mathrm{and} 1.50\pm 0.37$ eV, respectively. Each of these resonances was narrower than the estimated 2-keV spread in the proton beam. These two states are interpreted as the analogs of the ground and the second excited state of ${}_{}{}^{33}{}_{}{}^{}\mathrm{P}$ with $J^{\pi }$ values ${\frac{1}{2}}^{+}$ and ${\frac{5}{2}}^{+}$, respectively. $\gamma$ decay of the lower resonance, investigated with a Ge(Li) detector, shows >88% and <12% branchings to the first excited state and ground state of ${}_{}{}^{33}{}_{}{}^{}\mathrm{Cl}$, respectively. The $M1\mathrm{}$ strengths of these transitions are compared with those obtained from $\beta$ analog transitions and with the theoretical predictions based on the many-particle shell-model calculations.

The level structure of ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ar}$ has been investigated via the stripping reaction ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}\mathrm{}(d,p)\mathrm{}{}_{}{}^{39}{}_{}{}^{}\mathrm{Ar}$ at an incident deuteron energy of 10.064 MeV with an over-all experimental resolution of approximately 35 keV. Proton groups leading to 44 states of ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ar}$ with excitation energies up to 7.727 MeV have been identified. 30 of these states with excitation energies up to 6.488 MeV are neutron-bound. The orbital-angular-momentum-transfer values and the spectroscopic factors have been extracted for 28 of the observed neutron-bound states using zero-range distorted-wave Born-approximation (DWBA) calculations corrected for nonlocality of the optical potential and finite range in the local-energy approximation. One $l=0\mathrm{}$, one $l=2\mathrm{}$, twelve $l=3\mathrm{}$, and fourteen $l=1\mathrm{}$ transfer values are assigned. Spin assignments have been made on the basis of the conventional shell-model ordering of states, by comparison with the level structure of the isotonic nucleus ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ in the reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\mathrm{}(d,p)\mathrm{}{}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ and on the basis of the Lee-Schiffer effect. It is found that the conventional DWBA calculation with spin-orbit coupling reproduces the observed Lee-Schiffer effect for $l=1\mathrm{}$ states remarkably well. The results of the present investigation are in fair agreement with those of recent shell-model calculations.

Experimental cross sections for the first eight triton groups in the reaction ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}\mathrm{}(p,t)\mathrm{}{}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ have been measured over an angular range 10-168° (lab) at two incident proton energies, 25.4 and 26.8 MeV. Distorted-wave Born-approximation (DWBA) calculations were able to describe general trends in the angular distributions for low-lying states. However, higher-lying states showed dramatic rearward enhancement relative to the DWBA cross sections. Excitation functions of all eight triton groups have been measured at four angles over a beam energy range 24.96 to 27.20 MeV. The excitation functions are nearly flat for all states; further, the angular distributions show no large changes with energy. These data indicate that compound-nucleus effects are not dominant. Thus the results suggest that the population of the unnatural-parity $3^{+}$ state at 5.22-MeV excitation is primarily through a direct-reaction mechanism, possibly a multistep process such as those shown to be important in ($p,t$) reactions by Ascuitto and Glendenning. The roles of spin transfer and multistep effects in the transition to the 5.22-MeV $3^{+}$ state in ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$ were investigated, the latter being the more probable mode of excitation.

Resonances in the reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}(p,p^{\prime }){}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ from 3.35 to 5.21 MeV have been studied through the acquisition of proton excitation functions, proton angular distributions, and $p^{\prime }-\gamma$ angular correlations. Analysis has been accomplished with a simple single-resonance model in which the compound-nucleus formation is incoherent with direct-interaction effects. Most of the six resonances which were analyzed had $J^{\pi }={\frac{3}{2}}^{-}$; one had $J^{\pi }={\frac{5}{2}}^{+}$. These resonant levels of ${}_{}{}^{41}{}_{}{}^{}\mathrm{K}$ are interpreted as being isobaric analogs of levels of the parent nucleus ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ar}$ and are identified with known levels resulting from the reaction ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}\mathrm{}(d,p)\mathrm{}{}_{}{}^{41}{}_{}{}^{}\mathrm{Ar}$. The decay of the ${\frac{3}{2}}^{-}$ resonances to the $2^{+}$ 1461-keV excited level of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ occurs with mixing of $p_{\frac{3}{2}}$ and $p_{\frac{1}{2}}$ waves. Spectroscopic factors for each partial wave have been calculated. 97% of the [${\left(p_{\frac{3}{2}}\right)}_n{}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}\left(2^{+}\right)$] strength in the parent ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ar}$ has been identified. The ${\frac{5}{2}}^{+}$ resonance decays to the 1461-keV $2_1^{+}$ level by means of an $s_{\frac{1}{2}}$ wave, indicating the presence of a proton wave-function component in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ of the form ${\left(s_{\frac{1}{2}}^{}{}_{}{}^{-1\mathrm{}}d_{\frac{3}{2}}^{}{}_{}{}^{-2\mathrm{}}{d}_{\frac{5}{2}}\right)}_2$.

Simultaneous measurements of ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{31}{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}\mathrm{}(d,t)\mathrm{}{}_{}{}^{31}{}_{}{}^{}\mathrm{S}$ cross sections have been made at beam energies of 17.7, 20.8, and 23 MeV. The experimental angular distributions and charge asymmetries are adequately described in terms of distorted-wave Born approximation calculations. Spectroscopic factors are found to be the same for ($d,{}_{}{}^3{}_{}{}^{}\mathrm{He}$) and ($d,t$) reactions within an accuracy of 5%. Ratios of cross sections for transitions to the ground states are found to decrease from 4.6 at 17.7 MeV to 2.5 at 23 MeV. Included in the ratios is a calculated factor of 1.8, which is due to a difference between single-particle wave functions of the transferred proton and neutron. A numerical estimate of the isospin impurity of the ground state of ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$ is made from these differences.

The reaction ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}\mathrm{}(d,p)\mathrm{}{}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ has been investigated at a deuteron energy of 23 MeV. Distorted-wave analyses of the angular distributions for the low-lying states of ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ have been carried out for several sets of optical-model parameters. The spectroscopic factors obtained for states up to 2.66-MeV excitation in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ are in qualitative agreement with shell-model predictions. It is found, however, that the results of analysis are sensitive to the choice of parameters, and there is difficulty in extracting reliable quantitative spectroscopic information from this reaction without the use of information from other reactions.

Lifetimes for the 2nd through 12th excited states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$ have been obtained by use of the attenuated-Doppler-shift technique. Combining these results with previous information on this nucleus makes it possible to assign spins to all of the states that have been studied. All of the information is then compared with a shell-model calculation and with other theoretical descriptions that have been advanced.

We have investigated levels of ${\mathrm{Co}}^{58}$ up to 4.1-MeV excitation by studying ${\mathrm{Ni}}^{60}(d,\alpha ){\mathrm{Co}}^{58}$ at 17 MeV and the reactions ${\mathrm{Fe}}^{57}({\mathrm{He}}^3,d)$ and ${\mathrm{Co}}^{59}({\mathrm{He}}^3,\alpha )$ at 18-MeV bombarding energy using the University of Pittsburgh Van de Graaff accelerator. Angular distributions up to 80 and 45°, respectively, for the first two reactions were taken with position-sensitive counters and nuclear emulsions in the focal plane of the Enge split-pole spectrograph. Typical experimental resolutions were 9-14 keV. Angular distributions for over 110 levels were compared with distorted-wave Born-approximation calculations in order to extract orbital angular momentum transfers. Optical-model well parameters satisfying the "well-matching" condition gave improved agreement of ($d,\alpha$) calculations with experimental angular distributions. Spectroscopic factors were obtained for seventy ${\mathrm{Fe}}^{57}({\mathrm{He}}^3,d){\mathrm{Co}}^{58}$ transitions. We give $J^{\pi }$ assignments for nine levels and $J^{\pi }$ suggestions or limits for a total of 88 levels. Some low-lying ${\mathrm{Co}}^{58}$ levels can be described as ${\mathrm{Co}}^{56*}$ plus a "spectator" neutron pair. Comparison with shell-model calculations of McGrory suggests that noticeable ($\pi f_{\frac{7}{2}}^{}{}_{}{}^{-1\mathrm{}},\nu f_{\frac{7}{2}}^{}{}_{}{}^{-1\mathrm{}}$) strength appears in the ${\mathrm{Co}}^{58}$ spectrum for $4^{+}$ states at around 500 keV of excitation. About 11 states predicted by McGrory could be identified with those seen experimentally.

The reaction ${\mathrm{Si}}^{28}(p,\gamma ){\mathrm{P}}^{29}$ at the $E_p=5.834\mathrm{}$ MeV resonance was used to populate the ${\mathrm{P}}^{29}$ 8.38-MeV level, thought to be the first ${\mathrm{P}}^{29}$ level with $T=\frac{3}{2}$. A 32-${\mathrm{cm}}^3$ Ge(Li) counter was used to study the $\gamma$ radiations from this state; $\gamma$-ray energies (keV), together with the ${\mathrm{P}}^{29}$ transition assignment (MeV), and branching ratios (%) are: 7000.0 ± 1.8 (8.38 → 1.38), 15.3 ± 1.5; 6430.3 ± 2.6 (8.38 → 1.95), 54.1 ± 2.4; and 5962.3 ± 2.6 (8.38 → 2.42), 30.6 ± 2.0. A search was made for a $\gamma$-ray branch analogous to the 20% branch of the mirror level in ${\mathrm{Si}}^{29}$, 8.31 → 4.90 MeV. The limits on two branches suggested by known ${\mathrm{P}}^{29}$ spin and parity assignments are: 8.38 → 4.97, (25 ± 14)% and 8.38 → 5.30, <3.4% (2 standard deviations). Angular distributions were measured for the 8.38 → 1.38, 8.38 → 1.95, and 8.38 → 2.42 transitions; the analysis of these distributions restricts $J\left(8.38\right)\mathrm{}$ to $\frac{3}{2}$ or $\frac{5}{2}$, and provides $\gamma$-ray multipole-mixing ratios. The radiative decay of this level is compared with the radiative decay of the mirror level in the conjugate nucleus, ${\mathrm{Si}}^{29}$. Incidental measurements were made of the energies of the second and third excited states in ${\mathrm{P}}^{29}$: $E_x \left(\mathrm{keV}\right)=1950.0\mathrm{}\pm 1.3 \mathrm{and} 2421.7\pm 1.3$, respectively. The excitation energy of the $T=\frac{3}{2}$ level was found to be $E_x=8382.1\mathrm{}\pm 2.8$ keV.

Several new $1^{+}$ states in ${}_{}{}^{48,50}{}_{}{}^{}\mathrm{Sc}$ have been identified in the (${}_{}{}^3{}_{}{}^{}\mathrm{He},p$) reaction. From distorted-wave (DW) calculations, it appears that the total $1^{+}$ strength of ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$, relative to the strength of the ($f_{\frac{7}{2}}{p}_{\frac{3}{2}}$) $5^{+}$ ground state, is about a factor of 3 larger than predicted by calculations within the $1f-2p$ configuration space. In ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$ most of the $1^{+}$ strength is concentrated in one state, whereas ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ shows a strong fractionation effect. Such a large $1^{+}$ strength in ${}_{}{}^{50}{}_{}{}^{}\mathrm{Sc}$ cannot be accounted for by existing nuclear-structure calculations. Provided the DW argument holds true, the large $1^{+}$ strength may indicate a new feature in the spectroscopy of ${}_{}{}^{48,50}{}_{}{}^{}\mathrm{Sc}$ and possibly in other odd-odd nuclei in this mass region.

The reaction ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ has been investigated at 18 MeV. Several new spectroscopic assignments have been made for the states in ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ up to an excitation energy of 7 MeV. The spectrum is dominated by $1^{+}$, $2^{+}$, and $3^{+}$ states. The $1^{+}$-$7^{+}$ members of the ${\left(f_{\frac{7}{2}}\right)}^{-1\mathrm{}}{f}_{\frac{7}{2}}$ multiplet are very weakly populated and this result is consistent with distorted-wave Born-approximation calculations based on such a model. The presence of configuration mixing in the low-spin members of the multiplet is deduced from a distorted-wave analysis of the cross sections; in particular the 6.685-MeV $0^{+}$ $T=4\mathrm{}$ state (the analog of the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ ground state) was found to be populated about 5 times stronger than predicted by the simple ${\left(f_{\frac{7}{2}}\right)}^{-1\mathrm{}}{f}_{\frac{7}{2}}$ model. This enhancement factor is similar to the one found in the reaction ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}\mathrm{}(t,p)\mathrm{}{}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}(\mathrm{g}.\mathrm{s}.\mathrm{})$ and can be explained in terms of small admixtures of $2s-1d$ hole components in the ${}_{}{}^{46}{}_{}{}^{}\mathrm{Ca}$ ground state and of $2p-1f$ configurations in the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ ground-state wave functions.

The low-lying states of ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}$ have been investigated via Coulomb excitation using $\alpha$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ projectiles. 11 states up to 1515 keV, including three unreported levels at 481, 721, and 1093 keV, have been excited and their $B{\mathrm{}\left(E2\mathrm{}\right)\mathrm{}}_{\mathrm{ex}}$ values determined. The revealed complexity of the level structure of ${}_{}{}^{97}{}_{}{}^{}\mathrm{Mo}$ provides a strong argument against good closure of the $d_{\frac{5}{2}}$ shell at $N=56\mathrm{}$ in molybdenum.

The ($p,t$) reaction has been studied for targets of ${}_{}{}^{230,232}{}_{}{}^{}\mathrm{Th}$, ${}_{}{}^{234,236,238}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{242,244}{}_{}{}^{}\mathrm{Pu}$, ${}_{}{}^{248}{}_{}{}^{}\mathrm{Cm}$, ${}_{}{}^{182,184,186}{}_{}{}^{}\mathrm{W}$, and ${}_{}{}^{196}{}_{}{}^{}\mathrm{Pt}$. Uniformly strong (∼15% of ground-state cross section) transitions were found to populate excited $0^{+}$ states in all of the actinide nuclides. The observed $0^{+}$ states were previously known for five of the actinide nuclei, and in these cases the states were characterized by small $\alpha$-decay hindrance factors and large $E0\mathrm{}$ matrix elements. They have been previously classified as $\beta$ vibrations. The strong excitation of the $0^{+}$ states in the ($p,t$) reactions, combined with all other available evidence, suggests that throughout the actinide mass range these $0^{+}$ states represent a stable collective excitation different in character from both the $\beta$ vibration and the most common formulation of the pair vibration. No such excitations were seen in the W-Pt region.

Measurements of the decay from excited states in ${}_{}{}^{93}{}_{}{}^{}\mathrm{Mo}$ following sub-Coulomb stripping have been made using the reaction ${}_{}{}^{92}{}_{}{}^{}\mathrm{Mo}(d,p\gamma ){}_{}{}^{93}{}_{}{}^{}\mathrm{Mo}$ at an incident deuteron energy of 6.0 MeV. Both particle and $\gamma$-ray singles measurements were made using Si(Li) and Ge(Li) detectors. Proton-$\gamma$ coincidence spectra produced by 43 gates on proton groups associated with ${}_{}{}^{93}{}_{}{}^{}\mathrm{Mo}$ were accumulated by means of a two-parameter computer sorting program and yielded 24 levels with energies up to 5 MeV in excitation. A total in excess of 50 $\gamma$ rays was assigned to the deexcitation of levels in ${}_{}{}^{93}{}_{}{}^{}\mathrm{Mo}$. Branching ratios at ${\theta }_L=90\mathrm{}°$ are given for the transitions from the excited states along with a decay scheme observed following the ($d,p$) reaction.

The optical hyperfine structure and isotope shift in the 2537-Å line have been investigated. Two of the three components have been observed and measured. The magnetic-dipole-splitting factor $A\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ is -0.0771 ± 0.0005 ${\mathrm{cm}}^{-1\mathrm{}}$ and the isotope shift $\Delta S\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)$ is 0.112 ± 0.006 ${\mathrm{cm}}^{-1\mathrm{}}$ with respect to ${\mathrm{Hg}}^{198}$. The shift indicates staggering toward the heavier even isotope. An explanation is given in terms of nuclear deformation.

The rate of emission of $\alpha$ particles in coincidence with fission has been measured for ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ bombarded with protons of energy 16 and 42 MeV. There is a significant increase in the number of $\alpha$ particles per fission over this range. Part of this increase is due to contributions from the ($p,\alpha f$) reaction. After corrections are made for this process, however, there remains an increase of about 20% in the probability for the ($p,f\alpha$) reaction between the low- and high-energy measurements. These results together with those of others can be summarized by the formula $Y_{\alpha }=1.82\mathrm{}\pm 0.13+(0.019\pm 0.006)E^{*}$, where $Y_{\alpha }$ is the number of long-range $\alpha$ particles per thousand fissions and $E^{*}$ is the excitation energy. This dependence on energy can be understood by assuming that the $\alpha$ particles arise from the fragments that are most deformed at the scission point. Although the average deformation at scission remains approximately constant with excitation energy, the spread in the distribution of deformations and, hence, the number of configurations with high deformation, may increase with excitation energy. The angular correlation between fission fragments and $\alpha$ particles near 90° is independent of the excitation energy. At 180°, however, there is a marked increase in the number of coincidences as the excitation energy is increased.

Using the isotopic probability distributions of fragments as given by a model for the fission process and those of products as calculated from published product charge distribution parameters, a new procedure is developed for obtaining the number of neutrons $\overline{\nu }\mathrm{}(Z,N)\mathrm{}$ evaporated from individual fragments of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}(n_{\mathrm{th}},F)$. Following neutron evaporation as a cascade process and applying Weisskopf's evaporation theory to each step of the cascade, the excitation energy carried by the individual fragments is solved for from the $\overline{\nu }\mathrm{}(Z,N)\mathrm{}$ data. This procedure also gives an estimate of the fission $\gamma$ energy from individual fragments without an a priori assumption. The kinetic energy for each fragment is calculated from the total fission energy obtained using a mass formula and the computed excitation energy. Isobaric, isotopic, and isotonic averages of the parameters are presented.

The distributions of $\overline{\nu }\mathrm{}(Z,N)\mathrm{}$ versus $N$ for a given $Z$ show shell effects at neutron magic numbers $N=50\mathrm{} \mathrm{and} 82$. The maximum in isobaric average excitation energy for fragment pairs is found to occur a few mass units away from the point of symmetry, similar to such a trend observed in experimental $\overline{\nu }\mathrm{}\left(A\right)\mathrm{}$ for fragment pairs. The isotopic probability distributions given by the model do not take cognizance of any specific shell effects. However, from the minima in $\overline{\nu }\mathrm{}\left(Z\right)\mathrm{}$ and $\overline{\nu }\mathrm{}\left(N\right)\mathrm{}$ distributions in the region of magic numbers and the occurrence of peaks in the complementary regions, it is concluded that in fission events when a magic-number fragment is involved, the major part of the excitation energy is carried by the complementary fragment. The isobaric average kinetic energy distribution in the present work reproduces many of the fine structures in the experimental curve; however, the dip at the point of maximum excitation energy is not noticed in the latter. The fission-neutron spectrum in the laboratory frame is calculated from the spectra of evaporated neutrons from individual fragments and compared with the Watt spectrum. Average fission parameters obtained in the present work are in good agreement with experimental results.

In the "variable-moment-of-inertia" model an empirical relation was established between the transition quadrupole moments and the transition moments of inertia for the levels of ground-state bands in even-even nuclei. Later a modification was proposed in the form of introducing an explicit $A^{\frac{1}{4}}$ dependence in this relation, and also an alternative expression for the definition of the transition moment of inertia was adopted. We examine these modifications in comparison with the original assumptions through detailed analysis of the experimental data. No significant improvement in the fit to the data is observed as a result of the modified formulation.

The energy levels of ${}_{}{}^{25}{}_{}{}^{}\mathrm{Si}$ have been measured by detecting ${}_{}{}^6{}_{}{}^{}\mathrm{He}$ particles from the reaction ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$(${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{He}$)${}_{}{}^{25}{}_{}{}^{}\mathrm{Si}$ in photographic plates on the focal plane of a spectrometer. 12 excited states were observed. The observation of a weak state at 40-keV excitation leads to a new ${}_{}{}^{25}{}_{}{}^{}\mathrm{Si}$ ground-state mass excess, 3.824 ± 0.010 MeV. The observed levels are discussed in terms of the isobaric multiplet mass equation and the shell model.