Calculate the isotopic shift of the analogue states for Cr and Mn

[patric44]

Homework Statement

given the isotopic doublet Cr-Mn ,calculate the isotopic shift of the analogue states given the information below.

Relevant Equations

Ex> = Ex<+Exe+delta , where delta is the shift

hi guys
my nuclear physics professor gave us a hand written notes about a the isospin multiplets of elements, the notes provides a brief not clear introduction to the topic with some formulas for calculations, as following
$$
E_{xe} = \Delta\;E_{B}+\Delta\;E_{c}
$$
$$
\Delta\;E_{B}= E_{B}(z>,A)-E_{B}(z<,A)
$$
$$
\Delta\;E_{c}= 1.45*\frac{z>}{A^{1/3}}-1.03
$$
and finally
$$
E_{x>} = E_{x>}+E_{xe}+\delta
$$
the notes are very old and written by hand so its not clear, but i systematically manged to get through how to calculate the isotopic shift for the multiplet (B-C-N) in the example provided in the notes, However i found the following problem asking the same question :

is there is something missing in the given data, like where is Ex> and Ex< for Cr or Mn to calculate the isotopic shift??
is there are anyone familiar with this topic in nuclear physics , i will appreciate any help, also i was not able to find this topic as its with the given equations in any nuclear physics book that i knew, most of them talk about neutron proton isospin and T,Tz.

 

[patric44]

I just want to make sure, is it called the isobaric analogue states or the isotopic analogue states?, and can anyone suggest to me a book or some notes on the subject, i would really appreciate it

 

[Astronuc]

Definition - isobar, in nuclear physics, any member of a group of atomic or nuclear species all of which have the same mass number — that is, the same total number of protons and neutrons. Isotope refers to nuclides of the same element, i.e., some number of protons (and electrons in a neutral atom) and differing number of neutrons. Each nuclide ⁴⁷Cr and ⁴⁷Mn are radionuclides in general, and are isotopes (radioisotopes) of the respective elements, but they are isobars to one another. Both decay by electron capture. ⁴⁷Mn (88 ms) -> ⁴⁷Cr (500 ms) -> ⁴⁷V (32.6 min) -> ⁴⁷Ti (stable).

Cr has three stable isotopes/nuclides, ⁵²Cr, ⁵³Cr and ⁵⁴Cr, with ⁵⁰Cr is more or less stable due to a very long half life, est. >1.3E+18 y.

Mn has one stable isotope/nuclide ⁵⁵Mn.

Confirm with https://www.nndc.bnl.gov/nudat3/