Phosphorus is an important element for legume crop espacially for pea plant. In fact, phosphorus plays an immense role for nitrogen fixation. You ca find many articles in this case.
I was found from the researches, that the smaller plant growth at the low P levels did not result from N deficiency. The reduced nodulation and N, fixation in P-defident plants seem to be caused by impaired shoot metabolism and not by a direct effect of P deficiency of the nodules.
P deficiency reduces nodule biomass and N2 fixation relatively more than plant growth. From this it was inferred that the effect of P on N2 fixation was a direct one upon the nodules .
There is an early responses to P addition on shoot growth, nodulation and N2 fixation in subterranean clover and of the nature of the interaction between P and combined N2 on plant growth.
Some studies carried out on pea indicate that P deficiency impairs N, fixation in young pea plants indirectly by impairing the metabolism of the shoots and not by direct action on nodule formation or function. Phosphorous concentrations in nodules were largely unaffected by the P supply. Initially, P concentrations in shoots were much lower than concentrations in nodules at all levels of P supply. Phosphorus concentrations in shoots increased rapidly after P was supplied to P starved plants, but were still similar to, or slightly less than, concentrations in nodules.