J. Plasma Fusion Res. SERIES, Yol.2 (199\ 318-319

Three-Body Coulomb Resonances in Hydrogenic Plasmas
TOLSTIKHIN Oleg I., TOLSTIKHINA Inga Yu.,r'2 and NAMBA Chusei2Russian Research Center "Kurchatov Institute", Kurchatov sq. I, Moscow, 123182, Russia
tP. N. Lebedev Physical Institute,
2National Institute

Leninslq Prospect 53, Moscow, 117924, Russia
for Fusion Science, Toki 509-5292, Japan(Received: 7 December 1998 / Accepted: 23 March 1999)

Abstract
Results of a systematic study of the lowest r,S" Feshbach resonance in symmetric three-bodyCoulomb systems are reported. We found that the resonance width oscillates as a function of the mass-ratio of the constituting particles and maybe even vanishes at certain values this parameter. Theseoscillations are interpreted as a result of the interference between two different paths of the resonancedecay.

Keywords:
three-body Coulomb problem, resonance, H , Hi

With the increase of the density of particles thenegative atomic ions H- and the positive molecular ionsmore heavy (in atomic scale) particles, such as Hj. This

Hl become abundant in hydrogenic plasmas. Boththeory of resonances, have been resolved in the new
method based on Siegert PseudoStates (SPS) proposed
recently in [2] and further developed in [3]. The SPS
theory combines solid theoretical foundation with highcomputational efficiency and is able to provide reliabledifficulty, as well as some conceptual problems of thesystems play an important role in plasma diagnostics

and their spectroscopic observations may provide a
valuable information on plasma's characteristics Il].
However, while H is a well studied system the highprecision theoretical and experimental study of Hj is justin its beginning. In this work we initiate a systematic

results even in the situations where other methods fail,as was demonstrated in [2].

study of the lowest rS" Feshbach resonance inIn Fig. I we report our results of the SPS

calculations of the resonance position E.", and width fdefined by the resonance eigenvalue E = E,." - il/Z asfunctions of the mass-ratio between the heavy and thelight particles in the interval from I to 30. This interval

symmetric three-body Coulomb systems ranging fromH- to Hj.
Resonances constitute a very important class ofcollision phenomena revealing a complicated interplay
between attractive and repulsive forces acting in thecollision system. Formal theory of resonances has long
been completed by Breit and Wigner, Kapur and Pierles,Siegert, Feshbach, Fano, and many other authors.
Among the existing methods of resonance calculations
we mention the R-matrix theory, Kohn variational
principle, complex rotation and stabilization methods.
Each of these methods has its own merits, but they all
suffer from the common drawback of being unable totreat narrow resonances in systems containing two orcomplements our previous calculations for H- [2],includes the pptrt, dd1t, and ttp systems important for themuon catalyzed fusion project [4], and provides a one
more step towards the attack on Hj. We found that theresonance width oscillates with the variation of themass-ratio and maybe even vanishes at certain values ofthis parameter. Qualitative interpretation of these@1999 by The Japan Society of Plasma
Science and Nuclear Fusion Research318

Tolstikhin O.L et al., Three-Body Coulomb Resonances in Hydrogenic Plasmas

oscillations can be given within Fano-Feshbach(a)formalism and modern semiclassical theory. It can beshown that the oscillations result from an interference
between two paths of the decay of the resonance state.
One of these paths leads directly from the region oflocalization of the resonance wave function to thefragmentation region while the other one first passes
through the turning point on the lowest adiabatic
potential. The very small value of the resonance width at-0.'t0=

1 -o.tz
cbIUJ.

-0.14

PPlrt"...- , . ..tcertain values of the mass-ratio results from thedistructive interference of these two paths. This
indicates a very interesting possibility of existence ofbound state embedded in the continuum of the three-ddr

Wm

I eee

body Coulomb problem.

References(b)..;tll H. Tawara, NIFS-DATA-39 (National Institute forFusion Science, 1997).

1o-7iqLa'. PPl,t2) O.L Tolstikhin, V.N. Ostrovsky and H. Nakamura,Phys. Rev. Lett.79,2026 (1991).
t3l O.I. Tolstikhin, V.N. Ostrovsky and H. Nakamura,Phys. Rev. A.58,2077 (1998).
t4l J.S. Cohen in Review of Fundamental Processes
and Applications of Atoms and lons, ed. by C.D.

to't_ .t0-"
1oio'r tlp'10t1

Lin, World Scientific 1993, p.61.

1912051015202530
M/mFig. 1 The resonance position (a) and width (b) as
functions of the mass-ratio between the heavy
and the light particles. The realistic physicalsystems existing in this interval of Mlm areindicated in the figure.

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