The magnitude and the sign of spin-dependent scattering lengths of slow neutrons by nuclei of Li 7 , Al 27 , Sc 45 , Zr 91 , Nb 93 , La 139 , and Ta 181 have been determined by measuring the dependence of the precession angle of the neutron spins on the nuclear polarization of the scattering target.The scattering of slow neutrons by a fixed nucleus can be described by the scattering lengthwhere Ijy and s are the spins of the nucleus and the neutron, respectively. The parameter a N = (a + -a-)/(/# + !) (a + and «. being the nuclear scattering lengths of the nucleus for the two spin channels I N + \ and I N -i) is unknown for most nuclei. The growing use of polarized neutron beams, and targets with sizable polarizations obtained either in static fields at very low temperatures or by dynamic nuclear polarization, makes the knowledge of a N of greater interest. In this Letter, we report values of a N for a few nuclei.In analogy to neutron magnetic scattering, a new formalism has been introduced previously, and its physical validity experimentally demonstrated. 1 "* 3 It defines, inside a nuclear target, a pseudomagnetic field i/* produced by the pseudomagnetic moments M* of the target nuclei such thatwhere N is the number of nuclei per unit volume, P is their polarization, and jit* is given bywith jii B the Bohr magneton, r 0 = e 2 /mc 2 the classical radius of the electron, and^" = ii n /ii N = -1.913 the neutron magnetic moment expressed in nuclear magnetons. In a static field H 0 , the neutron magnetic moment will precess with the Larmor frequency o) L = -y n H 0 , where y n -2\i n /H= -2TT x 2 917 sec" 1 G" 1 is the gyromagnetic factor of the neutron. The effect of the pseudomagnetic fieldi/* is to change the Larmor precession frequency Co L of the neutrons inside the target by an amount Au). L = -y n H*, as first shown theoretically by Barytchevski and Podgoretzki. 4 A very sensitive method to measure small changes in precession frequency is through the change in the precession angle of the neutron polarization. Such a method has been described in a previous Letter. 5 The extra precession angle due to the pseudomagnetic field is a = -y n HH = -y n H*l/v y I being the sample length and v the neutron velocity. This extra precession angle is measured from the ratio R =I + /l" by the relation coso? = (l -R)/Dp 2 (l-eR),where I + and /" are the counting rates of the analyzer for opposite incoming-neutron polarizations (corrected for background), p 2 is the product of the polarizing and analyzing efficiencies, and e is the efficiency of the flipping coil used to reverse the incoming-neutron polarization. In our setup, p 2 = 0.990 andp 2 e = 0.981. The coefficient D takes into account any dephasing process resulting in a decrease of the measured polarization. It has been measured separately for each sample.The large pseudomagnetic moments of H 1 and V 51 give measurable precession angles even at 1 K. 5 But for many nuclei, M* is much smaller and, consequently, much higher polarizations are needed. Two somewhat compleme...