The ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^2{}_{}{}^{}\mathrm{C},p){}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ reaction has been used to study the reaction mechanism in the ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ system through the measurement of proton angular distributions. Angular distributions of protons emitted to nearly 70 states in ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ have been measured for three beam energies 29.5, 30.0, and 30.5 MeV. The energy region has been chosen as one not containing any "resonance" observed so far in this channel. Excitation functions for the energy range 29.0-30.8 MeV, with a $\Delta E=100\mathrm{}$ keV step, have been measured at a laboratory angle of 30°. Angular distributions for all incident energies exhibit strong structure which is preserved in averaged angular distributions. Comparison with the Hauser-Feshbach model is presented to show the deviation of the measured quantities from the statistical predictions. As the direct transfer of 11 nucleons and preequilibrium emission do not seem possible due to the small energy involved, the existence of another reaction mechanism is suggested.

[NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},p){}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$, $E_{\mathrm{lab}}=29.5,30.0,30.5\mathrm{}$ Mev. Measured $\sigma (E_p,\theta )$. Hauser-Feshbach calculations.]

A modified statistical analysis is proposed to account for the enhanced back angle scattering for certain heavy ion collisions. The fluctuation differential cross section, influenced by barrier top resonances, is predicted to approach a ${\left|P_{l_0}\right(\theta \left)\right|}^2$ form, where $l_0$ is the orbiting angular momentum. A statistical expression for the magnitude of the 180° fluctuation cross section is derived and applied to the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ elastic scattering at 30 MeV (c.m.). Numerical estimates, based on parameters in the literature, are found in qualitative agreement with observation.

[NUCLEAR REACTIONS Back angle enhancement in heavy ion elastic scattering. Modified statistical treatment. Estimates for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, 180° cross sections at $E_{\mathrm{c}.\mathrm{m}.\mathrm{}}=30\mathrm{}$ MeV. Barrier top resonances.]

We present an analysis of high energy heavy ion collisions at intermediate impact parameters, using a two-dimensional fluid-dynamical model including shear and bulk viscosity, heat conduction, a realistic treatment of the nuclear binding, and an analysis of the final thermal emission of free nucleons. We find large collective momentum transfer to projectile and target residues (the highly inelastic bounce-off effect) and explosion of the hot compressed shock zones formed during the impact. As the calculated azimuthal dependence of energy spectra and angular distributions of emitted nucleons depends strongly on the coefficients of viscosity and thermal conductivity, future exclusive measurements may allow for an experimental determination of these transport coefficients. The importance of $4\pi$ measurements with full azimuthal information is pointed out.

[NUCLEAR REACTIONS ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ + ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$, $E_{1\mathrm{ab}}=400\mathrm{}$ MeV/nucleon fluid dynamics, viscosity, heat conduction, cross sections.]

Trajectory calculations for head-on collisions of ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ + ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ and ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$ + ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ are performed based on several nucleus-nucleus potentials and the window formula for friction. Results are compared to the time-dependent Hartree-Fock calculations from literature in the same energy range.

[NUCLEAR REACTIONS Head-on classical trajectory calculations ${}_{}{}^{86}{}_{}{}^{}\mathrm{Kr}$ + ${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ at $E_{1\mathrm{ab}}=360-1000\mathrm{}$ MeV and ${}_{}{}^{84}{}_{}{}^{}\mathrm{Kr}$ + ${}_{}{}^{209}{}_{}{}^{}\mathrm{Bi}$ at $E_{1\mathrm{ab}}=500-1000\mathrm{}$ MeV.]

High spin states of ${}_{}{}^{75}{}_{}{}^{}\mathrm{Br}$ were studied through the ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni} ({}_{}{}^{16}{}_{}{}^{}\mathrm{O},2np)$ reaction. A positive and a negative parity band were established up to spin (25/2). A new low-lying isomeric (9/$2^{+}$) state ($T_{\frac{1}{2}}=39\mathrm{}\pm 4$ ns) at 220.6 keV excitation energy, most likely of $\tilde{\pi }{g}_{\frac{9}{2}}$ parentage, was found. The structure was interpreted in the light of the one quasiparticle plus rotor model concluding that the quadrupole deformation is largest for ${}_{}{}^{75}{}_{}{}^{}\mathrm{Br}$ compared to all other known odd Br isotopes.

[NUCLEAR REACTIONS ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},2np)$, $E=45-70\mathrm{}$ MeV. Measured $E_{\gamma }$, $I_{\gamma }$, $T_{\frac{1}{2}}$, $\gamma -\gamma$ coin. ${}_{}{}^{75}{}_{}{}^{}\mathrm{Br}$ deduced levels, $I^{\pi }$. Ge(Li) detectors, enriched target. Particleplus-rotor analysis. $\beta =0.31\mathrm{}$.]

The analyzing powers of heavy ion induced transfer reactions are discussed within the framework of the distortedwave Born approximation using a semiclassical model to describe the conservation of kinetic energy in the transfer process. It is found that the analyzing powers $T_{\mathrm{kq}}$ with $k$ odd have a strong dependence on $Q$ value. Those $T_{\mathrm{kq}}$ with $k$ even have a weaker $Q$ dependence and are specially sensitive to the deformed shape of the projectile. Strong $j$-dependent effects are found in the analyzing powers of (${}_{}{}^7{}_{}{}^{}\overrightarrow{\mathrm{L}}\mathrm{i}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$) reactions, particularly in $T_{2q}$ and $i{T}_{3q}$. Calculations for the ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^7{}_{}{}^{}\overrightarrow{\mathrm{L}}\mathrm{i},{}_{}{}^6{}_{}{}^{}\mathrm{Li}){}_{}{}^{59}{}_{}{}^{}\mathrm{Ni}$ reaction at $E_{\mathrm{Li}}=20.3\mathrm{}$ MeV are in good agreement with cross section and $i{T}_{11}$ angular distribution data.

[NUCLEAR REACTIONS: DWBA analysis of heavy ion induced transfer. ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^7{}_{}{}^{}\overrightarrow{\mathrm{L}}\mathrm{i},{}_{}{}^6{}_{}{}^{}\mathrm{Li}){}_{}{}^{59}{}_{}{}^{}\mathrm{Ni}$, $E=20.3\mathrm{}$ MeV; calculated $\sigma \left(\theta \right)$, $i{T}_{11}\left(\theta \right)$, $T_{2q}\left(\theta \right)$, $i{T}_{3q}\left(\theta \right)$, $j$-dependent effects.]

We study the correlation among $s$-wave low-energy four-nucleon observables by using a simplified dispersion theoretic ($\frac{N}{D}$) approach. We find that the triton binding energy, its asymptotic normalization parameter, the deuteron exchange left-hand cut, and the nucleon-trinucleon ($N-t$) scattering length control the low-energy $N-t$ system. The isospin one channel is insensitive to the asymptotic normalization parameter of the triton. The effective range function $kcot\delta$ for the isospin zero spin singlet $N-t$ system has a pole whose position and residue are strongly correlated with the $N-t$ scattering length. In this case the four-nucleon system (in our model) has an excited state whose binding energy and asymptotic normalization parameter are also correlated with the $N-t$ scattering length.

[NUCLEAR REACTIONS $s$-wave nucleon-trinucleon systems, spin-isospin channels, $\frac{N}{D}$ approach, low-energy correlations.]

The average Doppler shifts of characteristic $\gamma$ rays from nuclei produced in the ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ + ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ + ${}_{}{}^{20}{}_{}{}^{}\mathrm{Ne}$ reactions have been measured. Recoil velocities deduced from these data are shown to be sensitive to the heavy-ion reaction mechanism. Possible signatures of fusion-evaporation, direct-transfer or inelastic scattering, deep inelastic, and incomplete fusion processes are discussed.

[NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}({}_{}{}^{16}{}_{}{}^{}\mathrm{O},x)$; $E_{1\mathrm{ab}}=55-85\mathrm{}$ MeV; ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^{20}{}_{}{}^{}\mathrm{Ne},x)$; $E_{1\mathrm{ab}}=20-45\mathrm{}$ MeV; $\gamma$ ray Doppler shifts measured; reaction mechanisms discussed.]

High-spin states of ${}_{}{}^{76}{}_{}{}^{}\mathrm{Br}$ have been investigated through observations of $\gamma$ rays produced in the ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},pn)$ reaction by bombarding an enriched ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ target with 38.0-MeV ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ions. Measurements were made of $\gamma$-ray singles and $\gamma -\gamma$ coincidence spectra, $\gamma$-ray angular distributions, and $\gamma$-ray linear polarizations. Level energies, decay modes, spins and parities, $\gamma$-ray branching ratios, and $\gamma$-ray radiative admixtures were deduced. There is evidence for a strongly excited $\Delta J=1\mathrm{}$ quasirotational band.

[NUCLEAR REACTIONS ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}({}_{}{}^{12}{}_{}{}^{}\mathrm{C},pn) E=38\mathrm{}$ MeV; measured $E_{\gamma }$, $I_{\gamma }$, $\gamma \left(\theta \right)$, $\gamma$-ray linear polarizations; ${}_{}{}^{76}{}_{}{}^{}\mathrm{Br}$ deduced levels, $J$, $\pi$, $\delta$, $\gamma$ branching.]

In a recent work, the yields of spallation residues from 8-90 MeV proton induced fission of ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}$ were reproduced by exciton model calculations to which a fission option had been added. This allowed evaluation of the spectrum of fissioning nuclei. In this work, an extension of that calculation to the properties of the fission products is presented. Dividing the fissioning nuclei according to their fissionability, an approach is introduced which accounts for the percentage of symmetric and asymmetric fission, allows calculation of the most probable charge for a given fission product mass chain, and evaluates the numbers of pre- and post-fission neutrons. A comparison of the results of this calculation is made with extensive amounts of experimental data, and the implications of the calculation discussed.

[NUCLEAR REACTIONS, FISSION ${}_{}{}^{232}{}_{}{}^{}\mathrm{Th}\mathrm{}(p,f)\mathrm{} E=8-90\mathrm{}$ MeV; interpretation of mass distribution and charge dispersion based on calculations of model proposed.]

Absolute yields have been determined for 107 gamma rays emitted in the decay of 97 fission products representing 54 mass chains created during thermal-neutron fission of ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}$. These results include 14 mass chains for which no prior yield data exist. Using a Ge(Li) detector, spectra were obtained of gamma rays emanating from a 0.4 μg sample of ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}$ between 45 s and 0.4 yr after very short irradiations of the ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}$ by thermal neutrons. On the basis of measured gamma-ray yields and known nuclear data, total chain mass yields and relative uncertainties were obtained for 51 masses between 89 and 156. The absolute overall normalization uncertainty is ∼8%. The measured $A$-chain cumulative yields make up 77% of the total light mass ($A\le 123$) yield and 79% of the total heavy mass yield. The results are compared with fission-product yields previously measured, with generally good agreement. Information on the charge distribution along several isobaric mass chains was obtained by determining fractional yields for 11 fission products and combining these results with other measurements. The charge distribution width parameter for the heavy masses $A=128\mathrm{} \mathrm{to} 140$ is independent of mass to within the uncertainties of the measurements. For the light masses $A=89\mathrm{} \mathrm{to} 112$ the charge distribution parameter is also independent of mass but is smaller than for the heavy masses. Total chain yields are in fair agreement with the current evaluation for ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}$.

[RADIOACTIVITY, FISSION ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}\mathrm{}(n,f)\mathrm{} E_n=\mathrm{thermal}$; measured $\sigma (E_{\gamma },T_{\frac{1}{2}})$; deduced mass, charge yields.]

Analytic expressions are derived for the scattering amplitudes, in the Glauber approximation, for the Coulomb plus corresponding spin-orbit interaction, $V=V_c\mathrm{}\left(r\right)+\left(\frac{\lambda }{r}\right)\left(\frac{d{V}_c}{\mathrm{dr}}\right)({\overrightarrow{\sigma }}_1+{\overrightarrow{\sigma }}_2)·\overrightarrow{L}$, with $V_c=\frac{Z{e}^2}{r}$. The limiting cases of small momentum transfers or weak spin-orbit interactions are also presented as well as explicit expressions for the differential cross section, polarization, depolarization parameter, and various correlation parameters in these limits.

[NUCLEAR REACTIONS Scattering by a Coulomb plus spin-orbit potential, Glauber approximation, $\sigma \left(\theta \right)$, $P$, depolarization, parameter, correlation parameters.]

A systematic set of measurements of pion and proton yields from pion reactions on nuclei $4\le A\le 180$ has been performed for incident pions in the $\Delta \mathrm{}(3,3)\mathrm{}$ energy region. Detailed energy spectra for protons at many angles were obtained along with inclusive pion yields. The implications of general features of these data for the pion absorption and scattering processes are discussed.

[NUCLEAR REACTIONS ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$, ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Al}$, Ni, ${}_{}{}^{181}{}_{}{}^{}\mathrm{Ta}$, (${\pi }^{\pm },p$), (${\pi }^{\pm },{\pi }^{\pm \prime }$) inclusive; $E_{\pi \pm }=100,160,220\mathrm{}$ MeV; $30°<~\theta <~150°$; $\frac{d^2\sigma }{d\Omega d{E}_p},E_p\gtrsim 50$ MeV.]

Results of simple sequential model calculations are presented and compared with experimental data covering a wide variety of targets and energies. The model is fairly successful at higher energies (greater than about 200 MeV) but fails badly at lower energies.

[NUCLEAR REACTIONS (${\pi }^{+},{\pi }^{-}$) cross sections calculated and compared with experiment: $80 \mathrm{MeV}<~E_{\pi }<~300 \mathrm{MeV}$.]

We give an analytic expression for the in-medium nonstatic $\pi N$ transition matrix in nuclear matter. Pauli blocking and spreading effects are included explicitly. Spin-flip terms are retained. We discuss the modifications of the freespace amplitude as a function of energy and density and show that large dynamical isospin effects are expected in pion scattering on heavy nuclei.

NUCLEAR REACTIONS In-medium $\pi N$ transition matrix; isospin effects.]

Pion inelastic scattering at 180 MeV from the low-lying collective states of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ is analyzed using distorted-wave impulse approximation calculations with no free parameters and transition densities obtained from electron scattering. These calculations adequately reproduce the pion scattering data. No significant ${\pi }^{+}$ vs ${\pi }^{-}$ differences are observed at low-momentum transfers.

[NUCLEAR REACTIONS: ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({\pi }^{\pm },{\pi }^{{\pm }^{\prime }})$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({\pi }^{\pm },{\pi }^{{\pm }^{\prime }})$, $E_{\pi }=180\mathrm{}$ MeV. Measured $\sigma \left(\theta \right)$, DWIA analysis, ${\pi }^{+}$ vs ${\pi }^{-}$ comparisons.]

Starting from the nonexponential form of the high energy scattering amplitude introduced by Blankenbecler and Goldberger we derive a closed form approximation which tends to the exact Blankenbecler-Goldberger result for high momentum transfers. The present treatment is patterned closely after the work of Amado, Dedonder, and Lenz, appears to work just as well as their approximate form, and is analytically simple.

[NUCLEAR REACTIONS Closed form high-energy amplitude for hadron-nucleus scattering.]

Using the short pulses of a linac, a measurement has been performed of partial ${\mu }^{-}$-capture rates in ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ leading, respectively, to the bound excited states of ${}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{C}$. These rates are deduced from the intensities of the observed de-excitation nuclear $\gamma$ rays. A theoretical discussion is given based upon 1$p$-shell models and mesonic exchange currents.

[NUCLEAR REACTIONS Muon capture ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}(\mu ,\nu ){}_{}{}^{10}{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}(\mu ,\nu ){}_{}{}^{12}{}_{}{}^{}\mathrm{B}$, and ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}(\mu ,\nu ){}_{}{}^{14}{}_{}{}^{}\mathrm{C}$. Measured $I_{\gamma }$; Ge(Li) and hyperpure Ge detectors. Deduced partial capture rates. Mesonic exchange corrections and $1p$-shell models.]

The helium-jet recoil transfer technique has been used to study the decays of ${}_{}{}^{79}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{80}{}_{}{}^{}\mathrm{Y}$, ${}_{}{}^{81}{}_{}{}^{}\mathrm{Y}$, and ${}_{}{}^{82}{}_{}{}^{}\mathrm{Y}$, produced by ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{24}{}_{}{}^{}\mathrm{Mg},2pn)$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{24}{}_{}{}^{}\mathrm{Mg},pn)$, ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{25}{}_{}{}^{}\mathrm{Mg},pn)$, and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{24}{}_{}{}^{}\mathrm{Mg},pn)$ reactions, respectively. Decay properties of these four radioactivities have been deduced from the analysis of extensive singles and multiparameter spectroscopic measurements. The low lying level structure of ${}_{}{}^{80}{}_{}{}^{}\mathrm{Sr}$, as revealed by the decay of ${}_{}{}^{80}{}_{}{}^{}\mathrm{Y}$, can be reproduced through calculations of the interacting-boson-approximation model which place ${}_{}{}^{80}{}_{}{}^{}\mathrm{Sr}$ at or near the O(6) limit. Positron endpoint measurements [deduced from ($\beta ,\gamma$) coincidence studies] have been used to determine decay energies for each of these nuclides. Nuclidic mass excesses inferred from these data show progressively larger deviations from the predictions of currently available mass models for the more neutron-deficient $Y$ isotopes as the $N=Z$ line is approached. It is suggested that this may reflect the influence of nuclear deformation of these isotopes on the mass surface in the vicinity of $N=Z=40\mathrm{}$.

[RADIOACTIVITY ${}_{}{}^{79}{}_{}{}^{}\mathrm{Sr}$ from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{24}{}_{}{}^{}\mathrm{Mg},2pn)$; ${}_{}{}^{80}{}_{}{}^{}\mathrm{Y}$ from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{24}{}_{}{}^{}\mathrm{Mg},pn)$; ${}_{}{}^{81}{}_{}{}^{}\mathrm{Y}$ from ${}_{}{}^{58}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{25}{}_{}{}^{}\mathrm{Mg},pn)$; ${}_{}{}^{82}{}_{}{}^{}\mathrm{Y}$ from ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}({}_{}{}^{24}{}_{}{}^{}\mathrm{Mg},pn)$; measured $T_{\frac{1}{2}}$, $\sigma \mathrm{}\left(E\right)\mathrm{}$, $E_{\gamma }$, $E_x$, $E_{\beta }$, $I_{\gamma }$, $I_x$, $I_{\beta }$, ($\gamma ,\gamma ,t$), ($X,\gamma ,t$), ($\beta ,\gamma ,t$) coincidences; deduced levels, $J^{\pi }$, $Q_{\beta }$, mass excess, $log\mathrm{ft}$, He-jet system, enriched targets, Ge(Li), Ge and plastic detectors; comparison with mass predictions.]

Based on the variational principle in a general manifold in the Hilbert space and the principle of gauge invariance, the general gauge invariant periodic quantization method is formulated. This method, which is a direct generalization of the one previously obtained in the case of time-dependent Hartree-Fock, leads to a quantization rule which takes the Bohr-Sommerfeld form when the variational parameters are transformed to canonical variables. The method is illustrated by applying it to the manifold of minimum wave packets for a simple harmonic oscillator. It leads to the exact energy spectrum and a discrete set of wave packets which have maximum overlap with the exact eigenstates. The method is also applied to the exact Schrödinger dynamics where it exposes some open questions of the method.

[NUCLEAR STRUCTURE Time-dependent description of many-body bound states. Gauge invariant periodic quantization method, time-dependent variational principle and their canonical formulation.]