Sodium 2P fine-structure transitions in collisions with helium

Volume 6, number 2

CHEMKAL

SODIUM

‘P

PHYSICSLETTERS

FINE-STRUCTURE

IN CJOLLIgI0NS

I.5 July 1970

TRANSITIONS

WITH HELIUM

*

Received 19 May 1970 Based upon the interactionof Baylis, a close-coupled partiaGwave calculation of the cross section for fine-structure transitions in h’a(3pZP) in collisions with He has been carried out that _yields crass sections in harmony with the expernlmental vAIue. The agreement provides strong support of ffie theoretical description of the process and of the model used by Bsylis to calculate the interaction.

There has been a persistent discrepancy

be-

tween the experimental fl,2l$ and the calcuiated [3,4] values of the cross section for the j = 1/2 - 3/2 transitions in Na(3p2P) in collisions with He. The theoretical calculations are based on an orientation-dependent interaction, the quadrupole component of which can cause the transition. Semi-classical calculations [3] considered only the long range part of this interaotion and yielded results about one half of the experimental value, while a quanta1partial-wave anaIysis /41 in which a Lennard-Jones interac:tion was adopted gave a cross section one fourth of the experimentaf value. The present calculation uses the method described by Reid and i3algarno [4], who pointed ‘out that the close-couplirg analysis of Arthurs and Dalgarno [5] also describes the present problem provided the rigid-rotator wave function in the latter analysis is rephced by the internal wave function of Na(2P), ](Is)j). When the interaction is expanded in Legendre polynomials V(R) = T vJJR)P&J?)

2

position of the helium from the sodium nucleus and r is the position of the “ac-

where #? fs the

* Work partly supported by the National Aeronautics

and Space Administration under Grant No. NGL X2-007-136. $ Jordan and FraAkeA [1J measured the j = 3/Z -+.L/2 cross section. To obtain the.j = l/2 -+ S/2 cross seo- . tion, we multiplied their res@t by 1.92, &rich is the

detailedbatanuingfactor for this energy.

tive” electron,

onfg the g =O and g = 2 tern~s

contribute to the matrix elements for the channel wave functions, ](LS)jkTM),which describe states of total a&uIar momentum, J, formed by coupling the internal angular momentum of the sodium, j , to the orbita angular momentum, f . Tn our earlier work 141, ~6 and u2 had a Lennard-Jones form, Subsequent incLusion of the R-8 and R-10 pobxization Interaction increased the cross section, but for no reasonabIe welldepth did the cross section approach the experimental value. The rip and 7~2adopted in the present caIculation are those appropriate to the interaction derived by Baylis [6$ This interaction fncludes the higher order pofarieation terms but, more significantly, has large and comparatively long-range repulsive terms. The repulsive part OF~2 is considerably larger than that of ~6 for R greater th= 4~0. Fig, 1 shows the resulting cross section for the j = I/2 - 312 transition for barycentric impazt energies up to 0.07 et: The cwss section rises from zero at threshold to a maximum of 19.2 x 16-16cm2 at the impact energy E. = 0.031 eV. The maximum is broad and the cross section is larger than 76 x 10-16cm2 for the energy range 0.018 eV to 0.07 eV. This range corresponds to temperatures T.= 2E/3k from 140’K trj 640°K ZIlurearlier caicufations :Fperebased upon interactions that were more attractive than that given by SayIis and we predtcted the occurrence of a d&ailed structure dug to shape resonances, This stftseture may .appear for heavier Systems -. .

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PHYSICi LETTERS

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15 Jujy 1970

ature our &lcuJated d;;b& section iS 78.4 i lo-l8 cm2, in harmony with ttib measured dalues -of (78.9+5.6) x 10-16 cm2 rll and 66.0 x lO-l6cm2 ._ L J [2]_ It appea&: that it is the repulsive interaction which provides the main mechanism for the transition; +s had been suggested by Nikitin I?‘]. Its syccess in accounting for the observed cross sectioa provides strong support for the interaction models used by Bayiis. That the agreement is fortuitous cannot be excluded however. Experimental measurements of-the energy dependence’ of the cross section would provide a critical test. REFERENCES A. Jordan and P. A. Franken. Phys. Rev. 142 (1966) 20. [Z] 3.Pitre and L.Krause. Can. J. Phys. 45 (1967) 2671. f3] J. Caltaway and E. Bauer. Phys. Rev. 140 (l965) 1~1072; II. I. Mandklberg. in: Proc. Conf. Heavy Particle Collisions. Belfast. N.lreland (1968) (The Institute of Physics and the Physical Society. London, 1968) p. 177; L. Kumak and J. Callaway. Phys. Letters 28A (1968) [l! J.

-T-

‘LE/Sk(.K)

Fig: I. Computed cross secYon for Na(~p2P1/2) + He - Na(3p2P3/2) + He. but for Na-He with &ylis’ interaction it is replaced by a slow oscilktion, superimposed upon the overall trend of the cross section, giving lo. cal maxima at 0.019 eY, 0.031 eV and 0.048 eV. The energy at which the cross section is a decreasing function of energy has not been reached by the calculation. The crosk section was measured [l, 23 at a temperature of about 400°#, and at this temper-

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385. [Pj R. Ii. G. Reid ahd A. Dalgarno, Phys. Rev. Letters 22 (1969) 1029. [5J A.M. Arthurs and A. Dalgarno. Proc. Roy. Sot. A256 (L960) 540. 161 II’. E.Baylis, J. Chem.Phyk 51 (1969) 2665. [7] E. E. Nikitin. Opt. Spcctry. 22 (1967) 379.