Change in nuclear radius

Next to Fe, Sn is the second best Mossbauer isotope, in the sense that the y-ray energy, Mossbauer lifetime, and parent lifetime are all satisfactory. To use isomer shift measurements eflFectively, one must know the relative change in nuclear radius (8R/R). In the case of Sn, the correct value for this quantity was indefinite, both as to sign and magnitude. 

To get a fairly good number for the change in nuclear radius, we can consider a wider class of tin-containing materials. The results in Figure 1 are the work of Lees (12). Here we have taken arbitrarily as our origin, the source, the intermetallic compound Mg2Sn, which provides a convenient cubic environment for tin. It gives a line which has natural... 

The existence of a chemical isomer shift produced by the change in nuclear radius and differing chemical environments was first demonstrated by Kistner and Sunyar [15] in 1960 for the case of a stainless steel source and an absorber of a-FeaOs. Early work quickly showed that the chemical isomer shift measured was related to the formal oxidation state of the iron. This is illus-... 

As already discussed in some detail in Chapter 3, the magnitude of the chemical isomer shift depends not only on the values of the electron density at the tin nucleus for the compounds being compared, but also on the value of the fractional change in nuclear radius on excitation to the 23-88-keV level, 6R/R. Determination of the sign and magnitude of the nuclear constant dR/R has proved more difficult for Sn than for Fe because of the initial lack of accurate electronic wavefunctions for tin compounds. The various values which have been proposed are given in Table 14.1 in approximate chronological order [1, 23-29]. 

AR = change in nuclear radius Rq, -Roe = Sternheimer shielding factors Rfim =distancefrommthtonthion n = radial coordinate of ith electron rtj = distance from ith to /th nucleus [Pg.389]

Accurately calibrating the chemical isomer shift scale for a particular isotope is not without its difficulties. The change in nuclear radius, SR/R, cannot be determined independently of the chemical environment, which means that the electron density 1 s(0)P must be estimated by molecular orbital methods in at least two compounds before a value of SR/R can be obtained. 

Because the interactions measured in Mossbauer experiments are products of atomic and nuclear factors, experiments on iodine isotopes have yielded values of the change of nuclear radius between the ground state and the excited state, AR/R, quadrupole moment values Q, and magnetic moment values, fi, as well as electric field gradients and internal magnetic fields. 

Greater first IE than s-block elements due to increase in nuclear charge and small change in atomic radius... 

The relative change of the mean-square nuclear radius in going from the excited to the ground state, A r )/ r ), is positive for u. An increase in observed isomer shifts S therefore reflects an increase of the s-electron density at the Ru nucleus caused by either an increase in the number of s-valence electrons or a decrease in the number of shielding electrons, preferentially of d-character. 

The observed half-life of 238U is 4.47 x 109 y, which is a factor of 25 times longer than the calculated value. Note the qualitative aspects of this calculation. The a particle must hit the border of the parent nucleus 1038 times before it can escape. Also note the extreme sensitivity of this calculation to details of the nuclear radius. A 2% change in R changes A. by a factor of 2. In our example, we approximated R as 7 xh + Ra. In reality, the a particle has not fully separated from the daughter nucleus when they exit the barrier. One can correct for this by approximating R 1.4A1 3. 

The nucleons interact with each other by means of nuclear forces (the strong interaction), which leads to the formation of a dense nucleus with the radius 10 13 cm. In addition, the nucleons also interact with electrons and other nuclei of the molecule by means of electromagnetic forces, owing to which the nucleus takes part in the vibratory motion of the molecule. Since the electromagnetic forces are considerably weaker than the strong forces, they can only displace the nucleus as a whole but cannot produce any noticeable changes in the shape of the nucleon cloud. This means that the internal wave function of the nucleus depends weakly on the center-of-mass coordinate R4 and may be calculated for the equilibrium value R° of the latter. 

---