Golf ball having an over-indexed thermoplastic polyurethane elastomer cover and having a soft feeling when hit

1. A golf ball comprising:

a golf ball precursor comprising:

an inner core layer,

an outer core layer substantially surrounding the inner core layer, and

an inner cover layer substantially surrounding the outer core layer and having a first 100% modulus of greater than 300 kg/cm 2 ; and

an outer cover layer substantially surrounding the golf ball precursor and having a second 100% modulus of less than about 150 kg/cm 2 and a flexural modulus of less than about 800 psi;

the golf ball having a coefficient of restitution of less than 0.81;

wherein the outer cover layer comprises a cross-linked thermoplastic polyurethane elastomer including cross-links formed from allyl ether side groups, and the cross-linked thermoplastic polyurethane elastomer being the reaction product formed from reacting an organic isocyanate with a mixture of the following reactants:

(a) an unsaturated diol of the formula

in which R is alkyl group, and x and y are integers of 1 to 4;

(b) a chain extender, having at least two reaction sites with isocyanates and having a molecular weight of less than about 450;

(c) a long chain polyol having a molecular weight of between about 500 and about 4,000; and

(d) free radical initiator.

2. The golf ball according to claim 1 , wherein the unsaturated diol is trimethylolpropane monoallyl ether.

3. The golf ball according to claim 1 , wherein a molar ratio of the organic isocyanate moieties to the combination of the hydroxyl moieties of reactants (a) and (c) and the reaction sites of reactant (b)is from 1.06:1.00 to 1.18:1.00.

4. The golf ball according to claim 1 , wherein the outer cover layer has a flexural modulus of less than 600 psi.

5. The golf ball according to claim 1 , wherein the outer cover layer has a 100% modulus of less than 130 kg/cm 2 .

6. The golf ball according to claim 5 , wherein the outer cover layer has a 100% modulus of less than 100 kg/cm 2 .

7. The golf ball according to claim 1 , wherein the outer cover layer has a thickness of greater than about 1.0 mm.

8. The golf ball according to claim 5 , wherein the outer cover layer has a surface Shore D hardness of from about 50 to about 60.

9. The golf ball according to claim 1 , wherein the inner core layer comprises a highly neutralized acid polymer.

10. The golf ball according to claim 1 , wherein the inner core layer has a diameter of from about 21 mm to about 28 mm.

11. The golf ball according to claim 1 , wherein the inner core layer comprises an inorganic filler having a specific gravity of greater than 3 g/cm 3 .

12. The golf ball according to claim 1 , wherein the inner core layer has a compression deformation of from about 3.0 mm to about 4.5 mm.

13. The golf ball according to claim 1 , wherein the outer core layer comprises a polybutadiene rubber.

14. The golf ball according to claim 12 , wherein the outer core layer has a surface Shore D hardness which is greater than the surface Shore D hardness of the inner core layer.

15. The golf ball according to claim 1 , wherein the inner cover layer comprises a thermoplastic polyurethane.

16. The golf ball according to claim 5 , wherein the inner cover layer has a 100% modulus of greater than 320 kg/cm 2 .