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We study the mass neutrino interference phase in Schwarzschild-de Sitter space time along the null trajectory and the geodesic line and obtain the effects of cosmological constant Λ on the neutrino oscillation. Firstly, in the high energy limit, we find that the phase along the geodesic keeps the double of that along the null. Secondly, we calculate the phase on the condition that the cosmological constant, Λ, is a small quantity. The correction of the phase due to Λ is given. Finally, we calculate the proper oscillation length in Schwarzschild-de Sitter space-time, which increases because of the existence of Λ, compared with the result in Schwarzschild space-time. All of our results can be reduced to those in Schwarzschild space-time as Λ approaches to zero.

The plant mutation effects induced by ionizing radiation involve a rather complex process which is composed of physical, chemical, biochemical and biological stages. Nowadays, although ionizing radiation has been widely used in plant mutation breeding, the theoretical explanations for the mechanism of the ionizing radiation caused plant mutation effects are insufficient. Especially, a saddle shape relationship between the plant survival rate and radiation dose is found in the mutagenis effect of ionizing radiation on plants. The underlying mechanism of the saddle shape relationship remains unclear and challenges to all extant models.To explain this relationship, a damage-repair model for the plant mutation effects induced by ionizing radiation is proposed in the present work. Our model is based on the rate theory of ionizing radiation in which the cell damage and repair are taken into account simultaneously together with the micro-and macro-biological mutation effects of plant caused by ionizing radiation. The states of the radiated plant individuals are grouped into three categories: normal, damaged and lethal categories in our model. The evolution dynamics of the relative concentrations of the three categories are determined by a set of coupled equations which are mathematically the same as the Crow-Kimura equations in species evolution theories. With the numerical solution of our model in its steady state, the relative steady state concentration distributions of different categories of the radiated plants with increasing radiation dose are obtained. It is shown that without the plant repair effect, the relationship between the plant survival rate and radiation dose appears to be a conventional shoulder type one. With the plant repair effect, our model gives a saddle shape survival-dose relationship which has been observed commonly in the experiments on the radiated plants by ionizing radiation. To further test the model, the experimental data on the inbred lines of maizes radiated by heavy ion 7Li are used to determine the parameters of the model. It is shown that the theoretical results are basically consistent with the experimental ones. In addition, the mutation characteristic of the survival plants also appears to be a saddle effect-dose relationship, for which the theoretical model could also give a reasonable explanation. Our damage-repair model explains the saddle shape relationship between the plant survival rate and radiation dose, which indeed illuminates its power. And it provides a theoretical basis and reference for studying the biological effect mechanism of plants induced by ionizing radiation and conducting ionizing radiation plant breeding.

To explore the biological effects of the space radiation, dry seeds of mealycup sage (Salvia farinacea Benth.) were flown with the Chinese space craft “Shen Zhou VIII”. The plants grown from the space exposed seeds displayed considerable changes in phenotypic traits. Eleven space exposed plants (EP) showed one month longer flowering period than the mean of the control plants (CP); 13 EP failed to flower and 23 bore flowers, within which 25 plants mutated in respect of flower production; leaf shape of EP showed two extremes: curling and folding, or totally smooth; 11 EP had mutated height, within which 6 plants were taller and 5 shorter than CP. These results demonstrated that space radiation could induce favorable mutations on plant seeds.