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We study the dependence of the ground state energy on an appliedAharonov-Bohm flux $\Phi$ for the Luttinger model with large momentumscattering. Employing the method of finite size bosonization, we show that forsystems with a spin gap but with gapless charge degrees of freedom, the groundstate energy has an exact period of $hc/2e$, i. e. {\em half} a flux quantum,in the limit of large system size $L$. Finite size corrections are found tovanish exponentially in $L$. This behavior is contrasted to that of the spingapless case, for both even and odd particle number. Generalizations to finitetemperature are also discussed.Comment: 13 pages, 3 figures, RevTex4, published version, new Appendix on  proper use of canonical number-phase commutation relations in Klein factors  adde

The Luther-Emery liquid: Spin gap and anomalous flux period