A Continuum Theory of the Compound Nucleus

摘要: The nucleus is described by an absorption coefficient $\ensuremath{\sigma}$ which gives the probability per unit time that incident particle becomes amalgamated with (Eq. (1)). This appears as imaginary potential in Schr\"odinger equation. It shown a gradual decrease of at nuclear boundary essential for achieving agreement experiments (\textsection{}2). model automatically sticking fast neutrons, cross section proportional to $\frac{1}{v}$ slow and no one-particle resonances particles have penetrate barrier (\textsection{}3). Quantitative calculations are made varying ${e}^{\ensuremath{-}\frac{(r\ensuremath{-}R)}{b}}$ outside nucleus. For neutrons zero orbital momentum, formation compound found be $\ensuremath{\zeta}=1\ensuremath{-}{e}^{\ensuremath{-}2\ensuremath{\pi}\mathrm{kb}}$ where $k$ wave number. significant $\ensuremath{\zeta}$ depends on diffuseness $b$ rather than radius $R$. On other hand, factor $2\ensuremath{\pi}$ ensures close unity already energies about 1 Mev (\textsection{}4). total region overlapping levels, average level width separated levels expressed terms $\ensuremath{\zeta}$. relation elastic scattering discussed (\textsection{}5). case treated detail. With spacing $D$ 10 volts between same $J$, neutron $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{E}^{\frac{1}{2}}$ energy $E$, rough meager experimental data. these assumptions, will become larger radiation $E\ensuremath{\approx}{10}^{3}$ ev; capture "medium fast" ($\ensuremath{\approx}2\ifmmode\times\else\texttimes\fi{}{10}^{5}$ ev) can interpreted roughly this basis. equivalent from hard sphere whose ${R}^{\ensuremath{'}}$ defined condition $\ensuremath{\sigma}({R}^{\ensuremath{'}})=(\frac{\ensuremath{\hbar}}{2m{b}^{2}}){e}^{\ensuremath{-}2C}$ $C$ Euler's constant 0.577... (\textsection{}6). move non-nuclear $V$ (electrostatic or centrifugal) \textsection{}4, 7, 8 various relations $E$ height $V({R}^{\ensuremath{'}})$ barrier. If $E\ensuremath{-}V({R}^{\ensuremath{'}})$ more Mev, one, equal $V({R}^{\ensuremath{'}})$, still order (\textsection{}8). $ElV({R}^{\ensuremath{'}})$, contains well-known penetrability barrier, ${e}^{\ensuremath{-}2G}$, aside factors increase slowly $|E\ensuremath{-}V({R}^{\ensuremath{'}})|$ (\textsection{}7). magnitude inside derived extremely high Born approximation variation slight case. Although quantitative conclusions moderate cannot drawn, it seems likely least 20-40 (\textsection{}9). Finally, appreciable change results caused attractive repulsive added (\textsection{}10). In main part paper, has been assumed interaction zero.