C #AQMLP V1A 15-FEB-72. C LAST UPDATE: C FUNCTION AQMLP(N,ME,LE,K) C C *PURPOSE. C TO EVALUATE TRANSFORMATION COEFFICIENTS BETWEEN SPHERICAL C HARMONIC OSCILLATOR STATES AND CYLINDRICAL OSCILLATOR STATES. C THIS ROUTINE IS USED IN PARTICULAR BY "TBMOS3" IN THE CALCULATION C OF THE GENERAL MOSHINSKY BRACKET IN 3-DIMENSIONS. C C *PARAMETERS: C C N - INTEGER RADIAL QUANTUM NUMBER. C ME - INTEGER AZIMUTHAL COMPONENT OF ANGULAR MOMENTUM. C LE - INTEGER ANGULAR MOMENTUM QU-NR. C K - ADDITIONAL QUANTUM NUMBER - SEE BELOW. C C NOTE!! BY CONVENTION ALL ANGULAR MOMENTUM QUANTUM NUMBERS ARE C INTEGERS WITH TWICE THEIR PHYSICAL VALUES. THIS APPLIES TO "ME" C AND "LE" ABOVE. ALSO RADIAL QUANTUM NUMBERS ARE DEFINED SO "N"=0 C IS THE LOWEST STATE. C C NOTE: THE COEFFICIENTS ARE DEFINED BY THE PROPERTY: C C I N,L,M > = SIGMA [ A(Q,M,L,K) * I Q,M,K > ] C C WHERE THE SUM IS OVER "K" FROM "-M" TO "(Q-M)/2" EXCLUDING C NEGATIVE VALUES. THE STATE I N,L,M > IS A SPHERICAL OSCILLATOR C STATE WITH QU-NRS AS GIVEN ABOVE. THE STATE I Q,M,K > IS A C NORMALIZED CYLINDRICAL STATE BEING A PRODUCT OF 1-DIMENSIONAL C STATES AS: C IN THE Z DIRECTION (Q-M-2*K) QUANTA C IN THE (X+IY) DIRECTION (M+K) QUANTA C IN THE (X-IY) DIRECTION K QUANTA C THE QUANTUM NUMBER "Q" ABOVE IS "(2*N+L)" THE MAJOR SHELL NR. C C INPUT PARAMETERS: C N, ME, LE, K C OUTPUT PARAMETERS: C (REAL FUNCTION VALUE ONLY) C C *METHOD. C A SINGLE SUMMATION FORMULA INVOLVING FACTORIALS HAS C BEEN DERIVED BY D.M.BRINK. SEE NOTES TO "TBMOS3" FOR REFERENCES. C THE SUM IS EVALUATED BY DOING THE FIRST TERM EXPLICITLY C AND USING A SIMPLE RECURRENCE FOR SUCCESSIVE TERMS. C C *ACCURACY. C THIS HAS NOT BEEN TESTED IN DETAIL BUT IT IS BELIEVED THAT C THE MACHINE SIGNIFICANCE IS THE LIMITING FACTOR AT LEAST FOR C SMALL QUANTUM NUMBERS. C C *RESTRICTIONS. C THERE IS NO CHECK THAT THE QUANTUM NUMBERS MAKE PHYSICAL C SENSE! C C *ERROR CONDITIONS. C C *NON STANDARD ROUTINES CALLED. C FCTOR - FACTORIAL OF INTEGER ARGUMENT - MRMLIB C PARITY- + OR -1 AS ARGUMENT EVEN OR ODD - MRMLIB. C C *TYPICAL TIMES. C C *ORIGIN. C SEE NOTE ON "TBMOS3". THIS ROUTINE BY M.R.MANNING. C C *COMMENTS. C THE CYLINDRICAL STATES USED HERE IN THE DIMENSIONS X AND Y C ARE SIMPLY RELATED TO THE NORMAL ONES EXPRESSED IN TERMS OF C A RADIAL QU-NR AND THE AZIMUTHAL ONE "M". C C #END. C INTEGER Q,P,D,R AQMLP=0. L=LE/2 Q=N+N+L P=K M=ME/2 IF(M) 10,20,20 C ENSURE M POSITIVE 10 P=P+M M=-M 20 IF(M-L) 21,21,100 21 COM=FLOAT((LE+1)*2**(Q-M) )*FCTOR(N+L)*FCTOR(L+M) X *FCTOR(M+P)/FCTOR(Q+L+1) DIF=FCTOR(Q-M-P-P)*FCTOR(N)/(FCTOR(P)*FCTOR(L-M) ) D=P-N IF(D) 30,30,40 C TWO FORMS FOR FIRST TERM IN SERIES BEING SUMMED. C P.LE.N 30 TRM=PARITY(P)*SQRT(COM*DIF)/(FLOAT(2**(-D))*FCTOR(M)*FCTOR(-D) ) R=0 GO TO 50 C P.GT.N 40 TRM=PARITY(N)*SQRT(COM/DIF)/(FLOAT(2**D)*FCTOR(D)*FCTOR(M+D) ) R=D 50 AQMLP=AQMLP+TRM T=(P-R)*(R+R+M-L)*(R+R+1+M-L) IF(T) 100,100,55 55 R=R+1 S= 4*(R - D)*(R + M)*R TRM= -TRM*T/S GO TO 50 C 100 RETURN END