# lec08 - 22.101 Applied Nuclear Physics(Fall 2006 Lecture 8...

• Notes
• 7

This preview shows 1 out of 3 pages.

_______________________________________________________________________ ________________________________________________________________________ 22.101 Applied Nuclear Physics (Fall 2006) Lecture 8 (10/4/06) Neutron-Proton Scattering References : M. A. Preston, Physics of the Nucleus (Addison-Wesley, Reading, 1962). E. Segre, Nuclei and Particles (W. A. Benjamin, New York, 1965), Chap. X. We continue the study of the neutron-proton system by taking up the well-known problem of neutron scattering in hydrogen. The scattering cross section has been carefully measured to be 20.4 barns over a wide energy range. Our intent is to apply the method of phase shifts summarized in the preceding lecture to this problem. We see very quickly that the s-wave approximation (the condition of interaction at low energy) is very well justified in the neutron energy range of 1 - 1000 eV. The scattering-state solution, with E > 0, gives us the phase shift or equivalently the scattering length. This calculation yields a cross section of 2.3 barns which is considerably different from the experimental value. The reason for the discrepancy lies in the fact that we have not taken into account the spin-dependent nature of the n-p interaction. The neutron and proton spins can form two distinct spin configurations, the two spins being parallel (triplet state) or anti-parallel (singlet), each giving rise to a scattering length. When this is taken into account, the new estimate is quite close to the experimental value. The conclusion is therefore that n-p interaction is spin-dependent and that the anomalously large value of the hydrogen scattering cross section for neutrons is really due to this aspect of the nuclear force. For the scattering problem our task is to solve the radial wave equation for s-wave for solutions with E > 0. The interior and exterior solutions have the form ( ) = B sin( K r ' ) u r , r < r o (8.1) u r (8.2) and ( ) = C sin( kr + δ o ) , r > r o 1

Subscribe to view the full document.

( o h and k = where K ' = m V + E ) / mE / h . Applying the interface condition we obtain K 'cot( K r ' o ) = k cot( kr o + δ o ) (8.3)) which is the relation that allows the phase shift to be determined in terms of the potential parameters and the incoming energy E. We can simplify the task of estimating the phase shift by recalling that the phase shift is simply related to the scattering length by δ o = − ak (cf. (7.22)). Assuming the scattering length a is larger than r
You've reached the end of this preview.
• Spring '13
• AyhanYılmazer
• Proton, Neutron, Fundamental physics concepts, Nuclear physics

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern