Phonon Mediated Roton-Roton Interaction in Superfluid He 4

Progress of Theoretical Physics, Sep 1974

Roton-roton interaction mediated by phonon in superfluid helium is derived with use of the canonical transformation to eliminate the phonon-roton interaction introduced phenomenologically by Landau and Khalatnikov. The d-partial wave of this roton-roton interaction is examined which is relevant to the possibility of roton bound pair, observed in the experiment of Raman scattering. It is found that the coupling of d-wave may be attractive and be the order of magnitude, 10-39 erg·cm-3, for the roton minimum momentum. These results accord semi-quantitatively with the observed ones.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://ptp.oxfordjournals.org/content/52/3/777.full.pdf

Phonon Mediated Roton-Roton Interaction in Superfluid He 4

Phonon Mediated Roton-Roton Interaction in Superfluid He 0 0 Department of Physics, Nagoya University , Nagoya 1 > Present address: Department of Physics, Yokohama City University , Mutsuura, Kanazawa ku, Yokohama Raton-rotan interaction mediated by phonon in superfluid helium, is derived with use of the canonical transformation to elim'inate the phonon-rotan interaction introduced phenomenologically by Landau and Khalatnikov. The d-partial wave of this rotan-rotan interaction is examined which is relevant to the possibility of rotan bound pair, observed in the experiment of Raman scattering. It is fou1nd that the coupling of d-wave may_ be attractive and be the order of magnitude, 1o- erg'cm-, for the raton minimum momentum. These results accord semi-quantitatively with the observed ones. - 2. Phonon-roton interaction - (L) 2 (:~) { CP-PoYP' +p' CP__:Pof} + , H= :EEP<0lap+ap+ :Ecqb9 +b9 + Hi~~+H/!), p q Phonon Mediated Roton-Roton Interaction in Superjluid He' j'----;;-( q) jpq[(JLJCO) 1 8p0COJ 2pq qp+2 +. 2c Tp-2fJ.<0J ---ap X (lp+ql +P-2Po'01) - (2tJ-.1<O-J) 20/J.COJ {(ip+qi-PoC0lf,+ (P-Po(OJf}]. ap 3. Canonical transformation and roton-roton interaction S = z. .~.:...... A(p, q) p.q Ep - Ep+q + cq ap++qapbq +h.c. Ep=Ep(O)_ ~ A2(p+q, -q) q Ep+q-Ep + cq J -J<O) = _ ~ A 2 (Po+ q, -q) . q Ep,+q - Ep, + cq X a~+qa~--qap,ap + h.cJ We use the recent experimental data8l for the coupling parameters: ~ (:~) = -l.f Hr-r=- 21 A(p, q)A(p'-q, q) . (39) ' Phonon Mediated Ro_ton-Roton Interaction in Superfluid He4 4. Partial wave expansion of roton-roton interaction -d-~o c { (e e'lPo (E) +1- (3 + (e e'l) P2 (E) }, dEdQ 4 Wo (ph P2) = :E. (2l + 1) gz(PI, P2) Pz (cos ()), !(even) _.!_(8.d) (Ofl.) + rs(8Po) (Ofl.)} f1.2 8p Bp f1.3 8p 8p r=i'(Pl +P2-2Po), s=t{(Pl-PoY+ (p2-PoY}, t = {c CP/ + p22) _ r CP1-; P2Y}. fl. Phonon Mediated Roton-Roton Interaction in Superfiuid He' 5. Numerical value of d-wave coupling 92 = - .(8-.d)2-p2Xc (1. - Xc 2) 8p 2c 92 = _ PXc(1-Xc2) {(8.d) 2 +!L(BJJ.) 2 _!/_(O.d) (0/f.)'} 2c2 8p 4JJ.4 8p JJ.2 8p 8p 6. Summary Phonon Mediated Roton-Roton Interaction in Superjluid He4 References


This is a preview of a remote PDF: https://ptp.oxfordjournals.org/content/52/3/777.full.pdf

Koji Ishikawa, Kazuo Yamada. Phonon Mediated Roton-Roton Interaction in Superfluid He 4, Progress of Theoretical Physics, 1974, 777-785, DOI: 10.1143/PTP.52.777