Nuclear Magnetic Moment - Calculating The Magnetic Moment

Calculating The Magnetic Moment

In the shell model, the magnetic moment of a nucleon of total angular momentum j, orbital angular momentum l and spin s, is given by

By projecting with the total angular momentum j we get

has contributions both from the orbital angular momentum and the spin, with different coefficients g(l) and g(s):

by substituting this back to the formula above and rewriting

= {1\over (j+1)}\left(g^{(l)}{1\over 2} \left(j(j+1) + l(l+1) - s(s+1)\right) + g^{(s)}{1\over 2} \left(j(j+1) - l(l+1) + s(s+1)\right)\right)

For a single nucleon s =1/2. For we get

and for

Read more about this topic:  Nuclear Magnetic Moment

Famous quotes containing the words calculating the, calculating, magnetic and/or moment:

    “What our children have to fear is not the cars on the highways of tomorrow but our own pleasure in calculating the most elegant parameters of their deaths.”
    —J.G. (James Graham)

    “[The] elderly and timid single gentleman in Paris ... never drove down the Champs Elysees without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.”
    —Henry Brooks Adams (1838–1918)

    “We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate.”
    —Henry David Thoreau (1817–1862)

    “The moment when she crawled out onto the back of the open limousine in which her husband had been murdered was the first and last time the American people would see Jacqueline Bouvier Kennedy Onassis crawl.... She was the last great private public figure in this country. In a time of gilt and glitz and perpetual revelation, she was perpetually associated with that thing so difficult to describe yet so simple to recognize, the apotheosis of dignity.”
    —Anna Quindlen (b. 1952)