Reduced mass of nucleus

Rydberg constant (R - The fundamental constant which appears in the equation for the energy levels of hydrogen-like atoms i.e., E = hcR. 2 JrP-, where h is Planck s constant, c the speed of light, Z the atomic number, (Xthe reduced mass of nucleus and electron, and n the principal quantum number (n = 1,2,. ..). 

The scattering lengths discussed so far refer to a fixed nucleus. If the nucleus is free to vibrate, it will recoil under the impact of the neutron. In that case the effective mass is that of the compound nucleus, consisting of the neutron and the scattering nucleus. This means that the neutron mass m must be replaced by the reduced mass of the compound nucleus (i = mM/(M + m), where M is the mass of the scattering atom. As a result, the scattering length of the free atom is related to that of the bound atom by... 

The electronic stopping power involves a collision between the heavy ion nucleus and an electron of the medium. The reduced mass of the encounter can always be assumed to... 

One trivial improvement of the Dirac formula for the energy levels may easily be achieved if we take into account that, as was already discussed above, the electron motion in the Coulomb field is essentially nonreiativistic, and, hence, all contributions to the binding energy should contain as a factor the reduced mass of the electron-nucleus nonreiativistic system rather than the electron mass. Below we will consider the expression with the reduced mass factor... 

In the above calculation the system has been treated as though the nucleus were stationary and the electron moved in a circular orbit about the nucleus. The correct application of Newton s laws of motion to the problem of two particles with inverse-square force of attraction leads to the result that both particles move about their center of mass. The center of mass is the point on the line between the centers of the two particles such that the two radii are inversely proportional to the masses of the two particles. The equations for the Bohr orbits with consideration of motion of the nucleus are the same as those given above, except that the mass of the electron, m, is to be replaced by the reduced mass of the two particles, /, defined by the expression 1/m = 1/m + 1/M, where M is the mass of the nucleus. 

In this equation, jjl is the reduced mass of the system, and o-inv is the cross section for the inverse process in which the particle b is captured by the nucleus B where b has an energy, Eb. The symbols p(E B) and p( c) refer to the level density in the nucleus B excited to an excitation energy E% and the level density in the compound nucleus C excited to an excitation energy, . The inverse cross section can be calculated using the same formulas used to calculate the compound nucleus formation cross section. Using the Fermi gas model, we can calculate the level densities of the excited nucleus as... 

The expressions for the Bohr atom technically should use the reduced mass // = electron nucleus/ ( electron T- nucleus) instead of the electronmass, as noted in Equation 5.22. This alters the calculated value of the Bohr radius do, and therefore also alters the radius R and the total energy E = —Ze2/2R. 

All the symbols have their usual meanings. In the non-recoil limit, the motion of the nucleus is neglected and its finite mass enters only as a reduced mass of the electron. The additional terms arising from the dynamical effects of the nucleus, namely the recoil corrections and radiative-recoil corrections, have been omitted from equation 1 and will not be considered here. For more detailed discussions of the theory, see the review by Sapirstein and Yennie [3] and more recently [4,5,6], The expansion in (Za) is now carried out by expressing F and H as power series in (Za) and ln(Za) 2, as shown below in equations 2 and 3, where a is the ratio of the electron mass to its reduced mass. 

PROBLEM 3.1.2. Bohr s 1913 derivation of the energy of the hydrogen atom (nuclear charge = e, electron charge = e, reduced mass of the electron-nucleus couple = m, electron-nucleus distance = r, linear momentum = p) is based on the classical energy... 

PROBLEM 3.1.3. The energy of a one-electron atom (nuclear charge Z e, electron charge — e, reduced mass of the electron-nucleus couple p) is obtained by solving the Schrodinger equation for the one-electron atom ... 

The Rydberg constant equation has two terms that vary depending on the species under consideration, the reduced mass of the electron/nucleus combination and the charge of the nucleus (Z). 

The Don-adiabatic theory for a diatomic (r denotes the electronic coordinates, R stands for the vector connecting nucleus b with nucleus a, R = R, N means the number of electrons, m is the electron mass, V represents the Coulombic interaction of all particles, p, is the reduced mass of the two nuclei of masses Ma and Mj,). 

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