He3/(He3+He4) Ratios in Cosmic Rays, Path Lengths in Space, and Energy Spectrum of Helium Nuclei in Local Interstellar Space

Recent data on the ratios of ${\mathrm{He}}^3$/(${\mathrm{He}}^3$+${\mathrm{He}}^4$) in cosmic rays in the energy interval 45-300 MeV/nucleon in 1963-65 have been used to determine the path length of helium nuclei in space. In these calculations we have taken into account (i) the energy dependence of the cross sections for the production of ${\mathrm{He}}^3$ and ${\mathrm{H}}^3$ from $p+{\mathrm{He}}^4$ reactions and that of the total inelastic cross section as obtained from all available data, (ii) the ionization loss of ${\mathrm{He}}^4$ and ${\mathrm{He}}^3$ nuclei in space, and (iii) the solar modulation of the fluxes of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ nuclei. It is shown that using the data of the measured ${\mathrm{He}}^3$/(${\mathrm{He}}^3$+${\mathrm{He}}^4$) ratios, the accurately measured differential spectrum of He nuclei in the energy interval 30-1500 MeV/nucleon in 1965, and the $R\beta$ (i.e., rigidity × velocity) dependence of the solar modulation, we can determine both the path lengths in space and the residual solar modulation, and hence the energy spectrum of the He nuclei in local interstellar space, assuming a simple form of the source spectrum. The path lengths determined from ${\mathrm{He}}^3$/(${\mathrm{He}}^3$+${\mathrm{He}}^4$) ratios are in agreement with those from $\frac{\mathrm{Li}}{M}$ ratios ($M$-nuclei: $6<~Z<~9$). The path length of multiply charged nuclei in space is found to have a maximum value of about 7-9 g ${\mathrm{cm}}^{-2\mathrm{}}$ of hydrogen at 200-300 MeV/nucleon and to drop to about 2-3 g ${\mathrm{cm}}^{-2\mathrm{}}$ at 50 MeV/nucleon and to 3.5 g ${\mathrm{cm}}^{-2\mathrm{}}$ at 1000 MeV/nucleon. The source spectrum is found to be consistent with a power spectrum in rigidity, but not with a power spectrum of total energy per nucleon or power spectrum of kinetic energy per nucleon with an exponent of 2.5.