It is likely that matter in a neutron star crust is compressed by accreting matter and/or by the slowingdown of its rotation after the freezing of thermonuclear equilibrium. The change of nuclear compositions, which takes place during the compression, has been investigated. If the initial species of nuclei is Fe, the charge and the mass number of nuclei decrease as a result of repeated electron captures and successive neutron emissions in the initial stage of compression. The nuclear charge and mass are then doubled by pycnonuclear reactions. The final values of the charge numbers of the nuclei in the inner crust at densities p<10 13• 7 g/cm' are less than 25, which are about one third of those for the conventional cold catalyzed matter. This result reduces the shear modulus of the crust to one half of the conventional value which makes the magnitude of star quakes weaker. § l. lntroduction After the discovery of pulsars, the nuclei in the neutron star matter have been investigated in detail by many authors_v~sl The nuclei may form a crystal lattice and breaking of that lattice may be the explanation of a sudden change in the period of pulsars. Langer et al.,v Bethe, Borner and Sato,'l Baym, Bethe and Pethick 3l (hereafter denoted as BBP), and recently Mackie and Baym4) in vestigated the nuclei in the neutron star matter with the aid of extended mass formulae of nuclei. Buchler and Barkat 5l and Barkat, Buchler and Ingber 6) cal culated the spatial distributions of neutrons and protons in the neutron star matter with the aid of a Thomas-Fermi model of nuclei. More complicated Hartree-Fock calculations were carried out by Ravenhall, Bennet and Pethick,7l and Negele and Vautherin. 8l Theyv~s) obtained nuclear species as a function of the density of the neutron star matter. However they assumed that the neutron star matter is in its absolute ground state. This state is realized only if the matter has had sufficient time in the preceding hot stages of the star to reach nuclear equilibrium and no density changes occur thereafter. Bisnovatyi-Kogan and Chechetkin 9) discussed the r process nucleosynthesis in the neutron star crust assuming the existence of abundant neutrons in its hot stage. They calculated how the r-process proceeds when the density is fixed. Their calculations are essentially a simplified version of the r process computations in a strongly degenerate electron sea, 10)~14) in which both of the temperature and the density vary.